Extended Atomic Structure Calculations for W11+ and W13+

Singh, Narendra; Aggarwal, Sunny; Mohan, Man

doi:10.3390/atoms8040092

Open AccessArticle

Extended Atomic Structure Calculations for W¹¹⁺ and W¹³⁺

by

Narendra Singh

¹,

Sunny Aggarwal

^1,*

and

Man Mohan

²

¹

Department of Physics, Shyamlal College, University of Delhi, Delhi 110032, India

²

Department of Physics & Astrophysics, University of Delhi, Delhi 110007, India

^*

Author to whom correspondence should be addressed.

Atoms 2020, 8(4), 92; https://0-doi-org.brum.beds.ac.uk/10.3390/atoms8040092

Submission received: 1 August 2020 / Revised: 26 November 2020 / Accepted: 3 December 2020 / Published: 7 December 2020

(This article belongs to the Special Issue Atomic Structure Calculations of Complex Atoms)

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Abstract

:

We report an extensive and elaborate theoretical study of atomic properties for Pm-like and Eu-like Tungsten using Flexible Atomic Code (FAC). Excitation energies for 304 and 500 fine structure levels are presented respectively, for W¹¹⁺ and W¹³⁺. Properties of the 4f-core-excited states are evaluated. Different sets of configurations are used and the discrepancies in identifications of the ground level are discussed. We evaluate transition wavelength, transition probability, oscillator strength, and collisional excitation cross section for various transitions. Comparisons are made between our calculated values and previously available results, and good agreement has been achieved. We have predicted some new energy levels and transition data where no other experimental or theoretical results are available. The present set of results should be useful in line identification and interpretation of spectra as well as in modelling of fusion plasmas.

Keywords:

oscillator strength; FAC; NIST; EBIT; spectroscopy

PACS:

32.70; Cs oscillator strengths

1. Introduction

There has been strong interest in the spectroscopy of tungsten as it is planned to be used in plasma facing components of future fusion devices, such as International Thermonuclear Experimental Reactor (ITER) due to its favourable physical and chemical properties, e.g., high energy threshold of sputtering, low sputtering yield, low tritium retention, and high melting temperature [1,2]. Since tungsten is a high-Z element (Z = 74), where Z is the atomic number, it will contribute a large fraction of energy carried out from the plasma, which leads to plasma cooling. Atomic data such as energy levels, radiative transition rates, and photoionization cross sections for low-charged and medium-charged ions are of great importance in the ITER plasma diagnostics [3]. In the past few decades, atomic data for several highly charged tungsten ions have been determined using different experimental and theoretical methods [4,5,6,7,8], but still there is demand for more accurate atomic data, especially for low and medium ionization states of tungsten.

In the present work, spectra of moderately charged states of tungsten (W¹¹⁺ and W¹³⁺) are theoretically investigated. Several observations and theoretical calculations have been performed for Pm-like W but, for Eu-like W, only a few experimental data are available in the literature. In fact, only one theoretical energy value can be found for Eu-like W in the Atomic Spectra Database of the National Institute of Standards and Technology (NIST) [9]. These ionized states of tungsten are complex due to an open 4f shell, and obtaining accurate atomic data for these ions is a largely unsolved problem. For example, by inclusion of different configuration sets in the calculations, one will obtain a different ground state. The accuracy of a calculation can be estimated by considering (i) the convergence rate, (ii) the agreement between experimental measurements and theoretical calculations, and (iii) the difference between the velocity and length gauges of oscillator strength. Furthermore, results of calculations depend on the configuration-interaction (CI) effects, and, to ensure good accuracy, the most essential interactions must be included. In the past few years, we have calculated accurate atomic data by taking into account the essential interactions [10,11,12,13,14,15]. Brage and Froese Fischer [16] and Froese Fischer [17] presented a detailed review of analysis and evaluation of the CI effect in different atomic structure codes. In our present work, we have compared our calculated results with the available theoretical and experimental results and found good agreement.

2. Available Atomic Data

2.1. Pm-Like W (W¹³⁺)

Promethium-like ions have been studied both experimentally and theoretically over many years. There is still no full understanding of this sequence due to the open 4f shell, and obtaining accurate atomic data for this sequence is a largely unsolved problem. There is contradiction over the ground state for various charged states of Pm-like ions. Reliable atomic data for Pm-like ions are much needed, as some of these ions are promising candidates for the development of future optical clocks [18] and measurement of variation of the fine structure constant [19,20]. Curtis and Ellis [21] by their Hartree-Fock-Pauli (HFP) calculations showed that, in Pm-like W, the ground state is 4f¹⁴5s ²S_1/2 and dominant resonance lines are 5s-5p doublets. Theodosiou and Raftopoulos [22] performed a fully relativistic but single configuration calculation, using the Dirac-Fock approximation, and determined that the ground state of W¹³⁺ is odd parity 4f¹³5s^{2 2}F_7/2. Hutton et al. [23] identified the transitions 4f¹⁴5s ²S_1/2- 4f¹⁴5p ²P_1/2,3/2 using an electron beam ion trap (EBIT). Vilkas et al. [24] evaluated transition wavelengths and lifetimes in Pm-like ions (including W¹³⁺) by taking 4f¹³5s², 4f¹³5p², 4f¹³5s5p, 4f¹²5s²5p, 4f¹²5s5p², and 4f¹²5p³ configurations using relativistic multi-reference Møller-Plesset second order perturbation theory (MR-MP). They claim to have accuracy of a predicted wavelength of about 0.25 Å for Pm-like W. Their [24] work targeted the 4f¹⁴5s ²S_1/2- 4f¹⁴5p ²P_1/2,3/2 transitions between excited states.

Kramida and Shirai [25] predicted that the ground state of Pm-like W is 4f¹³5s^{2 2}F_7/2 while the first excited state is 4f¹³5s^{2 2}F_5/2, which is separated by 18,000 cm⁻¹ from the ground state. Wu and Hutton [26] discussed the behaviour of relative intensities of strong lines at different electron beam energies. Kramida [27] in his review noted the effect on the calculated energies from inclusion of two additional configurations (4f¹¹5s²5p² and 4f¹⁰5s²5p³). Safronova et al. [28] calculated excitation energies of some levels in Pm-like ions (including Pm-like W) using relativistic many body perturbation theory (RMBPT), Hebrew university Lawrence Livermore atomic code (HULLAC), and Hartree-Fock relativistic method (Cowan’s code). They confirmed that the ground state is 4f¹³5s^{2 2}F_7/2. Qiu et al. [29] studied the visible and soft X-ray spectral regions and concluded that 4f collapse is not complete in W¹³⁺. According to them [29], four lines that were identified in the Berlin EBIT spectra [30] do not appear to originate from tungsten. Kobayashi et al. [31] observed extreme ultraviolet and visible spectra of W¹³⁺ using EBIT. Zhao et al. [32] observed visible transitions in W¹³⁺ using Shanghai high temperature superconducting EBIT. They predicted that, out of eight observed lines, five belong to transitions from 4f¹²5s²5p. Recently, Ding et al. [33] calculated wavelengths and transition rates of the 5s-5p transitions of tungsten ions (including W¹³⁺) using the relativistic configuration interaction method as implemented in the Flexible Atomic Code (FAC) [34].

2.2. Eu-Like W (W¹¹⁺)

Ions of the Eu isoelectronic sequence (63 electron systems) are complex systems due to open 5s, 5p, and 4f subshells, but atomic structure calculations for these ions are needed to interpret the observed features. In the past, no extensive calculations for Eu-like W have been carried out. In fact, no spectral lines are available at the NIST website [9] for this particular ion. However, some authors reported selected transition wavelengths. Several studies contradict over the ground state for this ion. Kramida and Shirai [25] predicted that the ground state of Eu-like W is 4f¹³5s²5p^{2 4}F_7/2, while the first excited state is 4f¹⁴5s²5p ²P_1/2 located approximately 11,000 cm⁻¹ above it. They showed that the ground state of this ion is uncertain. Li et al. [30] reported spectra for some transitions in the range of 150–400 Å using the Shanghai high-temperature superconducting electron beam ion trap (SH-HtscEBIT). They have also performed calculations using the fully relativistic FAC using nine configurations, which generated 2538 fine-structure levels. They confirmed that the ground state is 4f¹³5s²5p^{2 4}F_7/2. Mita et al. [34] observed EUV spectra for multiple charged tungsten ions (including W¹¹⁺). They have compared experimental measurements with collisional-radiative (CR) model calculations.

3. Theoretical Method

In spite of calculations performed by different authors for Pm-like and Eu-like W, there are no medium-scale calculations for these ions, and the shortage of complete and accurate data for these ions motivates this work. Most past calculations included very limited CI with an arbitrary choice of configurations. Therefore, in the present work, extensive calculations for W¹¹⁺ and W¹³⁺ have been performed within the framework of FAC, which was developed by Gu [35]. FAC is a fully relativistic program used to compute the atomic structure, photoionization cross sections, and other atomic data. It is based on the Dirac-Hartree-Fock-Slater (DHFS) method, which uses perturbation theory. Optimization of orbitals is performed in a self-consistent-field iterative procedure in which the average energy of a fictitious mean configuration is minimized. This mean configuration represents the average electron cloud of the configurations retained in the CI expansion. In FAC, the Hamiltonian and configuration atomic state functions are similar to those of the MCDF (multi-configuration Dirac-Fock) method, including relativistic effects and higher-order QED effects, e.g., the Breit interaction in the zero-energy limit for the exchanged photon, and hydrogenic approximations for self-energy and vacuum polarization effects.

The effective Hamiltonian for an N-electron system is given by:

\hat{H} = \sum_{i = 1}^{N} {\hat{H}}_{i} + \sum_{i = 1}^{N - 1} \sum_{j = i + 1}^{N} V_{i j},

(1)

where

{\hat{H}}_{i}

is the Dirac one-particle operator for the ith-electron and V_ij represents effective electron-electron interactions.

An atomic state function (ASF) with total angular momentum J, its z-projection M, and parity p is assumed in the following form.

ψ_{s} (J M^{P}) = \sum_{m} c_{m} (s) ϕ (γ_{m} J M^{P})

(2)

where

ϕ (γ_{m} J M^{P})

are configuration state functions (CSF), c_m(s) are configuration mixing coefficients for the states, and

γ_{m}

represents all information required to uniquely define a certain CSF. A detailed description of this theoretical approach can be found in the literature [35].

4. Result and Discussion

4.1. Eu-Like W

There is scarcity of complete, consistent, and reliable atomic data for Eu-like W in the literature. Therefore, in the present calculations, we have evaluated energy levels and radiative transition rates using FAC for Eu-like W with a set of electronic configurations ([Kr]4d¹⁰) 4f¹²5s²5p5d², 4f¹²5s²5p²5d, 4f¹²5s²5p³, 4f¹²5s5p²5d², 4f¹³5s²5p5d, 4f¹³5s²5p², 4f¹³5p²5d², 4f¹³5s5p5d², 4f¹³5s5p²5d, 4f¹³5s5p³, 4f¹⁴5s²5d, 4f¹⁴5d5f², 4f¹⁴5d²5f, 4f¹⁴5d³, 4f¹⁴5s²5f, 4f¹⁴5f³, 4f¹⁴5s²5p, 4f¹⁴5p5d5f, 4f¹⁴5p5d², 4f¹⁴5p5f², 4f¹⁴5p²5d, 4f¹⁴5p²5f, 4f¹⁴5p³, 4f¹⁴5s5d², 4f¹⁴5s5f², 4f¹⁴5s5p5d, 4f¹⁴5s5p5f, and 4f¹⁴5s5p², which generate 20,573 fine structure levels. Previous studies have not included so many configurations. Our ground state with this set of configurations is 4f¹³5s²5p^{2 2}F_7/2, which is also shown by Li et al. [30].

We found complexity in the energy levels of Eu-like W. We have performed several calculations with different configurations included and found significant differences in the results, especially for the ground state. We are discussing one such difference. We have performed calculations by including the 4f¹⁴5l³ (l = s,p,d,f,g), 4f¹³5s²5p², 4f¹³5s5p³, 4f¹³5s²5p5d, 4f¹³5s5p²5d, 4f¹²5s²5p³, and 4f¹²5s²5p²5d configurations, which generate 4653 fine structure levels. Using these configurations, the ground state is found to be 4f¹⁴5s²5p ²P_1/2. This problem is due to an insufficient account for inter-electron correlations, as accurate calculation of energies of open-f-shell configurations requires accounting for single and double excitations not only from the valence shells (including 4f), but also from the core shells such as 4d, which makes the study of Eu-like W more difficult. Therefore, we decided to check the reliability of our calculated results by comparison with the other available theoretical and experimental results, as suggested by Froese Fischer [17].

We present energy levels (in Ryd.) of the lowest 304 levels in Table 1 calculated using FAC. In the column “configuration,” we give the configuration in LS coupling, while, in the “2J” column, the relativistic designation ending with the 2J value of a particular level is provided. Each shell is denoted so that 4f+7(7) represents seven electrons in the 4f_7/2 subshell (J = 7/2), and 4f-5(5) represents five electrons in the 4f_5/2 subshell (J = 5/2). The number in parentheses is two times the total angular momentum of the coupled shell. Immediately after the parentheses, there is a number indicating the 2J value obtained after all preceding shells are coupled. Completely filled relativistic subshells, such as (4f_5/2)⁶ and (5s_1/2)², are omitted in the ‘2J’ designations. For example, 4f+6(8)p+1(3)11 represents [(4f_5/2⁶)₀(4f_7/2⁶)₄(5s²)₀(5p_1/2²)₀(5p_3/2¹)_3/2] (J = 11/2).

A widely used method of accuracy assessment is to match the calculated results with the critically evaluated data compiled by National institute of Standard and Technology (NIST). For Eu-like W, there is only one energy value present in the Atomic Spectra Database (ASD) [9] for the level 4f¹⁴5s²5p ²P_1/2, which is 0.10 Rydberg (Ryd) with the uncertainty of 0.18 Ryd., while our calculated result for the same level is 0.105 Ryd. The NIST value was obtained in a very primitive Cowan-code (HFR) calculation made with only a few configurations included. Furthermore, Li et al. [36] reported the calculated value for the energies of the lowest 18 levels for W¹¹⁺. They have included 4f¹³5s²5p², 4f¹⁴5s²5p, 4f¹²5s²5p³, 4f¹³5s²5p5l, 4f¹³5s²5p6l, 4f¹²5p²5s²5l, 4f¹²5p²5s²6l, 4f¹⁴5s²5l, and 4f¹⁴5s²6l configurations, which generate 16,752 levels. The 4f¹⁴5s²5p ²P_1/2 level does not appear among their list of the lowest 18 levels, while, in our calculation, this is the second level, which is also suggested by Kramida and Shirai [25]. We have performed a calculation by taking the same configurations as Li et al. [37] and found that 4f¹⁴5s²5p ²P_1/2 is the second level, but they have not reported that. Our level designations for the first three levels are unambiguous, as the dominant eigenvector components constitute 96.3%, 97%, and 95.7%, respectively. For some levels, designations can be ambiguous due to mixing. The basis state given as the label of our calculated level 211 (59%) is mixed with that of level 217 (23%). Level designations of Li et al. [37] differ from our present calculation for some levels. This is because they have not included many important configurations within n = 5. Furthermore, for the 4f¹³5s²5p^{2 2}F°_7/2–²F°_5/2 transition, Li et al. [37] reported the transition wavelength calculated using FAC. They have also measured the transition wavelength for the same transition using SH-HtscEBIT, which is 527.60 ± 0.06 nm, while their calculated wavelength is 516.37 nm for the same transition. Our wavelength for this transition calculated using FAC is 472.06 nm.

In Table 2, we present a comparison of wavelengths calculated with FAC with other experimental and theoretical wavelengths [30] for the (4f¹³5s²5p²)_5/2–(4f¹³5s5p³)_3/2,5/2,7/2 transitions in Eu-like W, which is also shown in Figure 1. For all transitions, our calculated transition wavelengths agree with the experimental results of Li et al. [30] within 4.7%, while the theoretical results of Li et al. [30] deviate from their experimental results by up to 3.1%. Li et al. [30] also used FAC as in the present calculations, but with a different number of configurations. They have included the 4f¹⁴5s²5p, 4f¹⁴5s5p², 4f¹⁴5s5p5d, 4f¹³5s²5p², 4f¹³5s²5p5d, 4f¹³5s5p³, 4f¹³5s5p²5d, 4f¹²5s²5p³, and 4f¹²5s²5p²5d configurations, which generate 2538 fine structure levels.

Table 3 presents transition data for some strong electric dipole (E1) transitions (transition probability A > 10⁸ s⁻¹), respectively, from the ground state to various levels among the lowest 304 levels. We present a transition wavelength λ (in nm), a weighted oscillator strength gf (dimensionless) (both the length and velocity forms), and a transition rate A_ji (s⁻¹) calculated using FAC for Eu-like W. In Figure 2, a comparison of the ‘length’ and ‘velocity’ forms of gf (actually, results in the Babushkin and Coulomb gauges) is made for a few of the strongest transitions given in Table 3. One can see that the plot has the usual regular behaviour of increasing scatter with a decreasing line strength. However, for the strongest transitions, although the scatter is small, there is a systematic offset. The velocity form is smaller than the length form by 30%. Thus, all E1 transitions in Table 3 are estimated to have a common uncertainty of 30%.

Table 4 and Table 5 present transition data for magnetic dipole (M1) and magnetic quadrupole (M2) transitions from the ground state to some of the lowest 304 levels. We have presented transition wavelength λ (in nm), weighted oscillator strength gf (dimensionless), and transition rate A_ji (s⁻¹) calculated using FAC for Eu-like W. We predict new oscillator strength and transition probability data, where no other theoretical or experimental results are available, which will form the basis for future experimental work.

In Table 6, we provide collisional excitation cross-sections of Eu-like W from the ground state for the incident electron energy range of 65 to 125 eV. To the best of our knowledge, there are no other data points for collisional cross sections of Eu-like W in the literature within the given energy range.

4.2. Pm-Like W

Realizing the importance of Pm-like W and considering the paucity of atomic data for this ion, in the present work, we have calculated energy levels and radiative transition rates using FAC. To check the convergence of results, we have calculated results with different sets of configurations. Table 7 shows the configurations used in various calculations and the number of levels generated using these configurations. In the present work, we have increased the number of configurations in the sets in a systematic way to study the CI effect. In INP1, we have included 4f¹⁴5s, 4f¹³5s², 4f¹³5s5p, 4f¹⁴5p, and 4f¹³5p² configurations, which generate 59 fine structure levels. In INP2, we have added the 4f¹²5s²5p, 4f¹²5s5p², and 4f¹²5p³ configurations. These three configurations generate 621 levels. Furthermore, in order to check the effect on energies, INP3 forms a complex system by adding 4f¹¹5s²5p², 4f¹¹5s5p³, 4f¹⁰5s²5p³, and 4f¹⁰5s5p⁴ to INP2, which generates a total of 7790 fine structure levels. We observe that the energies of these additional configurations are distributed inside the interval between the 4f¹⁴5s and 4f¹⁴⁵p energies, which shows the importance of adding these configurations. Finally, in the INPF column of Table 7, we have considered a larger CI for Pm-like W, which includes 4f¹⁴5s, 4f¹³5s², 4f¹³5s5p, 4f¹⁴5p, 4f¹³5p², 4f¹²5s²5p, 4f¹²5s5p², 4f¹²5p³, 4f¹¹5s²5p², 4f¹¹5s5p³, 4f¹⁰5s²5p³, 4f¹⁰5s5p⁴, 4f¹²5s²5d, 4f¹²5s5d², 4f¹³5d², 4f¹³5p5d, 4f¹³5d², 4f¹³5p5d, 4f¹²5p5d², 4f¹²5p²5d, and 4f¹³5s5d configurations. This set generates 13,160 levels. Table 8 shows the list of configurations included and the number of fine structure levels arising from each configuration of Pm-like W. The ground state configuration in each case is the same. Table 9 lists the energy values from each input for the 4f¹³5s5p configuration. To check convergence, the difference between various output levels (Out1, Out2, Out3) and OutF is plotted in Figure 3. The different colors correspond to the different levels of Table 9. For levels 19 to 24, the difference is very large. Although the differences do not tend to zero with an increasing size of the calculation, the level splitting is almost the same in each output using different configuration sets for the first 18 levels, as shown in Figure 4. The root-mean-square (rms) difference from OUTF for the intervals ΔE_j is 0.16 eV for OUT1, 0.10 eV for OUT2, and 0.08 eV for OUT3.

Table 10 presents the energy levels (in Rydberg) for the lowest 500 levels calculated with FAC for Pm-like W. As can be seen from this table, we report results for many new levels that are not listed in the NIST tables [9]. The format of Table 10 is the same as in Table 1. Since 85 levels out of 500 of Table 8 have the same ‘2J’ label as some other levels, we report the eigenvector compositions and mixing coefficients of W¹³⁺ in Table S2 of the supplementary material. In this table, we report the composition of the levels given in Table 10. In the column, the ‘Comp. No.’ of Table S2 contains sequential numbers of the basis states in decreasing order of contribution. We have included only a few basis states with the largest contributions. For each basis state, Table S2 gives an electronic configuration in the JJ coupling scheme. In these designations, ‘4f13’ represents that there are 13 electrons in the 4f subshell. In ‘4f+7(7)7,’ the ‘+’ sign denotes the larger of the two possible values of the angular momentum for the f electron, i.e., ‘4f+’ corresponds to 4f7/2. ‘7’ after the ‘+’ sign shows the number of electrons in the relativistic subshell 4f7/2, ‘(7),’ which means that the total 2J value of the 4f7/2 subshell is 7, and ‘7’ at the end denotes the final 2J value of the configuration.

In Table 11, some of the calculated energies are compared with those from critically evaluated data compiled by NIST [9], which are commonly used as a reference set for atomic results. The calculated values of Safronova et al. [28] and Zhou et al. [32] are also presented for comparison in Table 11. For the level 4f¹³5s^{2 2}F_5/2, our calculated value matches the results of Zhou et al. [32]. For this level, the NIST value is from Vilkas et al. [24] whose results have been proven wrong by many authors in the recent past. They have used the MR-MP method for their calculation. For the 4f¹³5s5p levels, the maximum difference between our calculation using FAC and the calculation of Safronova et al. [28] is 3.1%.

In Table 12, we present the transition data for the 4f¹³5s^2–4f¹³5s5p and 4f¹⁴5s-4f¹⁴5p transitions including transition wavelengths (in nm), transition probabilities (A_ji in s⁻¹), and oscillator strengths (gf_ij, dimensionless). We give the oscillator strengths both in the velocity and length forms to check the accuracy of the calculated results, as it is one of the criteria used to assess the accuracy. The ratio of the velocity and length forms of the oscillator strength should be close to unity in accurate calculations. It is a necessary condition, even though it is not sufficient. As one can see in Table 12, this ratio is close to unity for most of the strong transitions. It is plotted in Figure 5 against line strength. For the Pm-like W, the systematic offset between the length and velocity forms is significantly smaller, at only about 10%. Therefore, the strongest E1 transitions with the line strength S_V > 0.017 a.u. can be assigned an uncertainty of 10%. Those with 0.004 a.u. < S_V < 0.017 a.u. can be assigned an uncertainty of 15%, and weaker transitions can be estimated as accurate to 30%. In Table 12, we also present the transition rates from the OUT3 results for comparison since, for magnetic transitions, the velocity form is not available. From Table 12, one can see that transition rates of OUTF have large differences from OUT3 for many levels, which is due to additional configurations in OUTF. In Table S1 of the supplementary material, we report M1 and E2 transition data for the transitions to various levels for 4f¹²5s²5p of Pm-like W, as these transitions could help to analyze experimental EBIT and tokamak spectra.

In the 4f¹³5s^{2 2}F_7/2 and 4f¹³5s^{2 2}F_5/2 levels, the mixing is very low, and their labeling is unambiguous. For both levels, the dominant eigenvector component contributes 98.3% and 98.4%, respectively. We would also like to mention that mixing among some of the levels is strong in our calculations. We found that level 250 is strongly coupled with level 317 with percentages of the corresponding components of 71% and 23%, respectively. We found that the level 277 is composed of 52% of the basis state used in its label mixed with 39% of the state used to label the level 357. Similarly, mixing among some other levels is very strong. Hence, the labeling of a particular level is not always based on the dominant eigenvector component. The configuration and J values given in Table 8 are definite, but the labels are not unique and can be interchanged.

Table S1 provides the means to estimate the uncertainties of the M1 and E2 transitions in Pm-like W. For example, Figure 6 plots the natural logarithm of the ratio A_outF/A_out3 of the E2 transition rates calculated in the two largest calculations. From this figure, one can see that, except for a few strongly discrepant transitions, the two data sets agree with each other fairly well. This figure is consistent with a typical behavior of calculated transition rates. For the strongest transitions (in this case, S_outF > 0.94 a.u.), the mean (i.e., root-mean-square, rms) of the logarithmic ratio is 0.014, corresponding to an agreement within 1.4% on average. For weaker transitions, the scatter of the data points increases, but, even for the weakest transitions with S < 0.00212 a.u., the mean disagreement is only 52%.

For M1 transitions, if three strongly discrepant transitions are excluded, the comparison of out3 and outF looks qualitatively similar, as shown in Figure 7. Here again, the strongest transitions (S_outF > 2.8 a.u. in this case) exhibit a mean discrepancy of 3.2%, while, for weaker transitions, it increases, but, even for the weakest transitions with S < 0.1 a.u., the mean discrepancy is only 15%. The three transitions excluded from this plot are 47 → 38, 65 → 38, and 74 → 38. For them, the discrepancies amount to a factor between 10 and 100.

In Table 13, we compare transition wavelengths (in nm) calculated using FAC with the data compiled by NIST [9] and with experimental and theoretical results of Kobayashi et al. [31] along with theoretical results of Safronova et al. [28] and Ding et al. [33]. For the transitions 0–91, 0–263, and 0–326, our calculated transition wavelengths are comparable (maximum difference of 5%) with the data compiled by NIST. For the transitions 0–433, 0–434, and 0–451, our calculated transition wavelength agrees well with the experimental results of Kobayashi et al. [31] (error within 0.4%) and are more accurate than the theoretical results of Safronova et al. [28] and Kobayashi et al. [31]. Furthermore, our calculated transition wavelengths for all transitions are in excellent agreement with the recent results of Ding et al. [33]. This is a clear indication of accuracy of our results.

In Table 14, we have compared transition wavelength (in nm) calculated with FAC for the transition 4f¹³5s^{2 2}F_5/2–²F_7/2 with other results for Pm-like W. The theoretical wavelengths are calculated in vacuum, while the experimental wavelengths are measured in standard air. Li et al. [30] and Zhao et al. [32] in Shanghai and Kobayashi et al. [31] in Tokyo observed similar spectra, but the charge state assignments differ by one. Recently, the Shanghai group confirmed [36] that their assignment made in References [30,32] was wrong and confirmed the assignment in Reference [31]. In addition, recent theoretical calculations by Ding et al. [33] also support the assignment in Reference [31]. Our theoretical result agrees within 2% with the experimental wavelengths of Kobayashi et al. [31]. This is better than the result of Safronova et al. [28], who used the COWAN code, and Vilkas et al. [24]. The differences of those two results from the measurement of Kobayashi et al. are larger (4% and 30%, respectively). The maximum discrepancy of 29% is between the experimental wavelength and the results of Vilkas et al. [24], which are responsible for discrepancies between our calculated results and the NIST data [9] quoted from Vilkas et al. [24]. Furthermore, our transition wavelength is in good agreement with the recent results of Ding et al. [33] as well as with other theoretical results listed in Table 14. In Table 15, we give the collisional excitation cross-sections of Pm-like W from the ground state for incident electron energy ranging from 45 to 75 eV. The collision cross section is given in units of 100 Mb.

5. Conclusions

Motivated by the need of atomic data for fusion plasma research, in the present paper, we have reported energy levels and radiative data, such as transition wavelengths and oscillator strengths, as well as collisional excitation cross sections for W¹¹⁺ and W¹³⁺. For the calculations, the fully relativistic FAC has been adopted with the inclusion of CI. The effect of CI has been examined and investigated systematically by including different configurations. The present calculations provide new energy level data and are useful for accuracy assessments. Based on several comparisons with NIST and other available results, our listed energies are accurate (error <1%) for most levels of both ions. Energies have been listed for the lowest 304 and 500 levels of W¹¹⁺ and W¹³⁺, respectively, but the remaining data for higher levels can be obtained from the authors on request. We have also presented radiative transition rates for both ions that are expected to be highly useful in analysis and modeling of plasmas. We have presented oscillator strengths in both velocity and length forms for both ions. We have compared our calculated data with the other available theoretical and experimental data and no (major) discrepancies have been found, except for some levels of Pm-like W calculated by Vilkas et al. [24]. Furthermore, we observed discrepancies in the ground state of Eu-like W, which depends on the configurations included. There is scope for further work in these complex systems.

Supplementary Materials

The following are available online at https://0-www-mdpi-com.brum.beds.ac.uk/2218-2004/8/4/92/s1. Table S1: Magnetic dipole (M1) and electric quadrupole (E2) transition data for transitions within the 4f13.5s2 and 4f12.5s2.5p configurations of Pm-like W. Table S2: Eigenvector compositions and mixing coefficients for Pm-like W.

Author Contributions

All authors have contributed equally in preparation of the manuscript. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by IAEA grant number 23244.

Acknowledgments

We are thankful to IAEA for providing financial support through a research coordination project entitled “Atomic data for vapour shielding in fusion devices” contract no. 23244. “Drafts of Figure 2, Figure 3, Figure 4, Figure 5, Figure 6 and Figure 7, as well as Tables S1 and S2 of the Supplementary Materials, were made for us by an anonymous Reviewer, whose help in preparation of this article for publication is gratefully acknowledged”.

Conflicts of Interest

The authors declare no conflict of interest.

References

Matthews, G.; Coad, P.; Greuner, H.; Hill, M.; Hirai, T.; Likonen, J.; Maier, H.; Mayer, M.; Neu, R.; Philipps, V.; et al. Development of divertor tungsten coatings for the JET ITER-like wall. J. Nucl. Mater. 2009, 390, 934–937. [Google Scholar] [CrossRef] [Green Version]
Hirai, T.; Escourbiac, F.; Carpentier-Chouchana, S.; Fedosov, A.; Ferrand, L.; Jokinen, T.; Komarov, V.; Kukushkin, A.; Merola, M.; Mitteau, R.; et al. ITER tungsten divertor design development and qualification program. Fusion Eng. Des. 2013, 88, 1798–1801. [Google Scholar] [CrossRef]
Clementson, J.; Lennartsson, T.; Beiersdorfer, P. Extreme Ultraviolet Spectra of Few-Times Ionized Tungsten for Divertor Plasma Diagnostics. Atoms 2015, 3, 407–421. [Google Scholar] [CrossRef] [Green Version]
Radtke, R.; Biedermann, C.; Schwob, J.L.; Mandelbaum, P.; Doron, R. Line and band emission from tungsten ions with charge 21+ to 45+ in the 45–70–Å range. Phys. Rev. A 2001, 64, 012720. [Google Scholar] [CrossRef]
Harte, C.S.; Suzuki, C.; Kato, T.; Sakaue, H.; Kato, D.; Sato, K.; Tamura, N.; Sudo, S.; D’Arcy, R.; Sokell, E.; et al. Tungsten spectra recorded at the LHD and comparison with calculations. J. Phys. B At. Mol. Opt. Phys. 2010, 43, 205004. [Google Scholar] [CrossRef]
Suzuki, C.; Koike, F.; Murakami, I.; Tamura, N.; Sudo, S.; Sakaue, H.A.; Nakamura, N.; Morita, S.; Goto, M.; Kato, D.; et al. EUV spectroscopy of highly charged high Z ions in the Large Helical Device plasmas. Phys. Scripta 2014, 89, 114009. [Google Scholar] [CrossRef]
Jonauskas, V.; Kučas, S.; Karazija, R. On the interpretation of the intense emission of tungsten ions at about 5 nm. J. Phys. B At. Mol. Opt. Phys. 2007, 40, 2179–2188. [Google Scholar] [CrossRef]
Jonauskas, V.; Kisielius, R.; Kynienė, A.; Kučas, S.; Norrington, P.H. Magnetic dipole transitions in 4 d N configurations of tungsten ions. Phys. Rev. A 2010, 81, 012506. [Google Scholar] [CrossRef]
Kramida, A.; Ralchenko, Y. Reader and NIST ASD Team 2019. Version 5.7.1. Available online: https://physics.nist.gov/asd (accessed on 8 October 2019).
Singh, A.K.; Aggarwal, S.; Mohan, M. Level energies, lifetimes and radiative rates in the 4p44d configurations of bromine-like ions. Phys. Scr. 2013, 88, 35301. [Google Scholar] [CrossRef]
Goyal, A.; Khatri, I.; Aggarwal, S.; Singh, A.; Mohan, M. Atomic structure calculations for Br-like ions. Can. J. Phys. 2015, 93, 487–495. [Google Scholar] [CrossRef]
Goyal, A.; Khatri, I.; Aggarwal, S.; Singh, A.; Mohan, M. Atomic structure calculations and identification of EUV and SXR spectral lines in Sr XXX. J. Quant. Spectrosc. Radiat. Transf. 2015, 161, 157–170. [Google Scholar] [CrossRef]
Goyal, A.; Khatri, I.; Aggarwal, S.; Singh, A.K.; Sharma, R.; Mohan, M. Collisional excitation of Florine like Tungsten using relativistic Dirac atomic R-matrix method. JAMNCP 2015, 2, 1. [Google Scholar]
Goyal, A.; Khatri, I.; Aggarwal, S.; Singh, A.K.; Mohan, M. Calculation of energy levels, lifetimes and radiative data for La XXIX to Sm XXXIV. At. Data Nucl. Data Tables 2016, 107, 406. [Google Scholar] [CrossRef]
Aggarwal, S.; Singh, J.; Mohan, M. Atomic structure calculations for Br-like ions. At. Data Nucl. Data Tables 2013, 99, 394. [Google Scholar] [CrossRef]
Brage, T.; Froese Fischer, C.; Brage, T. Systematic calculations of correlation in complex ions. PhysicaScripta 1993, T47, 18. [Google Scholar] [CrossRef]
Fischer, C.F. Correlation effects on transition probabilities in Mo vi. J. Phys. B At. Mol. Opt. Phys. 2011, 44, 125001. [Google Scholar] [CrossRef]
Berengut, J.C.; Dzuba, V.A.; Flambaum, V.V.; Ong, A. Highly charged ions with E1, M1, and E2 transitions within laser range. Phys. Rev. A 2012, 86, 22517. [Google Scholar] [CrossRef] [Green Version]
Berengut, J.C.; Dzuba, V.A.; Flambaum, V.V. Enhanced Laboratory Sensitivity to Variation of the Fine-Structure Constant using Highly Charged Ions. Phys. Rev. Lett. 2010, 105, 120801. [Google Scholar] [CrossRef]
Berengut, J.C.; Dzuba, V.A.; Flambaum, V.V.; Ong, A. Electron-hole transitions in multiply charged ions for precision laser spectroscopy and searching for variations in α. Phys. Rev. Lett. 2011, 106, 210802. [Google Scholar] [CrossRef] [Green Version]
Curtis, L.J.; Ellis, D.G. Alkalilike spectra in the promethium isoelectronic sequence. Phys. Rev. Lett. 1980, 45, 2099. [Google Scholar] [CrossRef]
Theodosiou, C.E.; Raftopoulos, V. Further studies of the promethium isoelectronic sequence. Phys. Rev. A 1983, 28, 1186–1188. [Google Scholar] [CrossRef]
Hutton, R.; Zou, Y.; Almandos, J.R.; Biedermann, R.; Radtke, R.; Greier, A.; Neu, R. EBIT Spectroscopy of Pm-like Tungsten. Nucl. Instrum. Methods Phys. Res B 2003, 205, 114. [Google Scholar] [CrossRef]
Vilkas, M.J.; Ishikawa, Y.; Träbert, E. Electric-dipole 5 s—5 p transitions in promethiumlike ions. Phys. Rev. A 2008, 77, 42510. [Google Scholar] [CrossRef] [Green Version]
Kramida, A.; Shirai, T. Energy levels and spectral lines of tungsten, W III through W LXXIV. At. Data Nucl. Data Tables 2009, 95, 305–474. [Google Scholar] [CrossRef]
Wu, S.; Hutton, R. Applications of EBITs to spectra of multi-electron ions: Some solved and some unsolved problems. Can. J. Phys. 2008, 86, 125. [Google Scholar] [CrossRef]
Kramida, A. Recent progress in spectroscopy of tungsten1This review is part of a Special Issue on the 10th International Colloquium on Atomic Spectra and Oscillator Strengths for Astrophysical and Laboratory Plasmas. Can. J. Phys. 2011, 89, 551–570. [Google Scholar] [CrossRef]
Safronova, U.I.; Safronova, A.S.; Beiersdorfer, P. Contribution of the 4f -core-excited states in determination of atomic properties in the promethium isoelectronic sequence. Phys. Rev. A 2013, 88, 32512. [Google Scholar] [CrossRef]
Qiu, M.L.; Li, W.; Zhao, Z.Z.; Yang, Y.; Xiao, J.; Brage, T.; Hutton, R.; Zou, Y. Review of highly charged tungsten spectroscopy research using low energy EBITs at the Shanghai EBIT laboratory. J. Phys. B At. Mol. Opt. Phys. 2015, 48, 144029. [Google Scholar] [CrossRef]
Li, W.; Shi, Z.; Yang, Y.; Xiao, J.; Brage, T.; Hutton, R.; Zou, Y. Tungsten spectroscopy in the EUV range observed at a high-temperature superconducting electron-beam ion trap. Phys. Rev. A 2015, 91, 62501. [Google Scholar] [CrossRef]
Kobayashi, Y.; Kubota, K.; Omote, K.; Komatsu, A.; Sakoda, J.; Minoshima, M.; Kato, D.; Li, J.; Sakaue, H.A.; Murakami, I.; et al. Extreme ultraviolet and visible spectroscopy of promethiumlike heavy ions. Phys. Rev. A 2015, 92, 022510. [Google Scholar] [CrossRef] [Green Version]
Zhao, Z.; Qiu, M.L.; Zhao, R.F.; Li, W.X.; Guo, X.L.; Xiao, J.; Chen, C.Y.; Zou, Y.; Hutton, R. Experimental and theoretical study of visible transitions in promethium-like tungsten. J. Phys. B At. Mol. Opt. Phys. 2015, 48, 115004. [Google Scholar] [CrossRef]
Ding, X.; Zhang, F.; Yang, Y.; Zhang, L.; Koike, F.; Murakami, I.; Kato, D.; Sakaue, H.A.; Nakamura, N.; Dong, C. Collisional-radiative modeling of the 5 p—5 s spectrum of W xiv–W xvi ions. Phys. Rev. A 2020, 101, 42509. [Google Scholar] [CrossRef]
Mita, M.; Sakaue, H.A.; Kato, D.; Murakami, I.; Nakamura, N. Extreme ultraviolet spectra of multiply charged tungsten ions. J. Phys. Conf. Ser. 2017, 875, 12019. [Google Scholar] [CrossRef]
Gu, M.F. The flexible atomic code. Can. J. Phys. 2008, 86, 675–689. [Google Scholar] [CrossRef]
Liang, S.; Lu, Q.; Wang, X.; Yang, Y.; Yao, K.; Shen, Y.; Wei, B.; Xiao, J.; Chen, S.; Zhou, P.; et al. A low-energy compact Shanghai-Wuhan electron beam ion trap for extraction of highly charged ions. Rev. Sci. Instrum. 2019, 90, 93301. [Google Scholar] [CrossRef] [Green Version]
Li, M.; Qiu, M.; Xiao, J.; Yao, K.; Brage, T.; Hutton, R.; Zou, Y. A strong visible line in the spectrum of W11+. Phys. Scr. 2016, 91, 105401. [Google Scholar] [CrossRef]
Nandy, D.K.; Sahoo, B.K. Highly charged W13+, Ir16+, and Pt17+ ions as promising optical clock candidates for probing variations of the fine-structure constant. Phys. Rev. A 2016, 94, 032504. [Google Scholar] [CrossRef]

Figure 1. Comparison of theoretical wavelengths with the experimental wavelengths of Reference [30].

Figure 2. A comparison of the length and velocity forms of oscillator strengths for a few of the strongest transitions of W¹¹⁺.

Figure 3. Difference of energy values of each output OUTn (n = 1, 2, 3) from the final calculation for the 4f¹³5s5p configuration.

Figure 4. Differences of energy intervals relative to the lowest level (with index 1) for each output OUTn (n = 1, 2, 3) from the final calculation for the 4f135s5p configuration.

Figure 5. A comparison of the velocity and length forms of oscillator strength for a few of the strongest transitions (E1) of W¹³⁺.

Figure 6. Natural logarithm of the ratio A_outF/A_out3 of the E2 transition rates calculated in the two largest calculations for W¹³⁺. The horizontal axis contains the line strengths S_outF of the largest calculation in atomic units.

Figure 7. Natural logarithm of the ratio A_outF/A_out3 of the M1 transition rates calculated in the two largest calculations for W¹³⁺. The horizontal axis contains the line strengths S_outF of the largest calculation in atomic units.

Table 1. Energies (in eV) of 304 lowest levels of Eu-like W.

Level	Configuration	2J	Energy (eV)
0	4f¹³5s²5p²	4f+7(7)7	0.000000
1	4f¹⁴5s²5p¹	5p-1(1)1	1.487410
2	4f¹³5s²5p²	4f-5(5)5	2.635751
3	4f¹³5s²5p²	4f+7(7)7.5p-1(1)6.5p+1(3)9	10.406621
4	4f¹³5s²5p²	4f+7(7)7.5p-1(1)8.5p+1(3)5	11.338412
5	4f¹³5s²5p²	4f+7(7)7.5p-1(1)6.5p+1(3)3	11.495144
6	4f¹³5s²5p²	4f+7(7)7.5p-1(1)8.5p+1(3)7	11.982615
7	4f¹³5s²5p²	4f-5(5)5.5p-1(1)6.5p+1(3)3	12.116363
8	4f¹³5s²5p²	4f+7(7)7.5p-1(1)8.5p+1(3)11	12.306080
9	4f¹³5s²5p²	4f+7(7)7.5p-1(1)6.5p+1(3)5	12.599174
10	4f¹³5s²5p²	4f+7(7)7.5p-1(1)8.5p+1(3)9	12.897008
11	4f¹³5s²5p²	4f+7(7)7.5p-1(1)6.5p+1(3)7	12.986980
12	4f¹²5s²5p³	4f+6(12)12.5p+1(3)15	13.168432
13	4f¹³5s²5p²	4f-5(5)5.5p-1(1)4.5p+1(3)7	13.903781
14	4f¹³5s²5p²	4f-5(5)5.5p-1(1)6.5p+1(3)5	14.122897
15	4f¹²5s²5p³	4f+6(8)8.5p+1(3)11	14.291251
16	4f¹³5s²5p²	4f-5(5)5.5p-1(1)6.5p+1(3)9	14.621510
17	4f¹²5s²5p³	4f+6(12)12.5p+1(3)13	14.631127
18	4f¹³5s²5p²	4f-5(5)5.5p-1(1)4.5p+1(3)1	14.679897
19	4f¹²5s²5p³	4f+6(8)8.5p+1(3)9	14.759824
20	4f¹²5s²5p³	4f-5(5)5.4f+7(7)10.5p+1(3)7	15.082206
21	4f¹³5s²5p²	4f+7(7)7.5p-1(1)8.5p+1(3)9	15.398633
22	4f¹²5s²5p³	4f+6(8)8.5p+1(3)11	15.501744
23	4f¹³5s²5p²	4f-5(5)5.5p-1(1)4.5p+1(3)5	15.508532
24	4f¹⁴5s²5p¹	5p+1(3)3	15.538168
25	4f¹²5s²5p³	4f+6(8)8.5p+1(3)7	15.864304
26	4f¹³5s²5p²	4f-5(5)5.5p-1(1)4.5p+1(3)3	15.922657
27	4f¹²5s²5p³	4f-5(5)5.4f+7(7)10.5p+1(3)13	16.076542
28	4f¹²5s²5p³	4f+6(8)8.5p+1(3)5	16.145582
29	4f¹²5s²5p³	4f-5(5)5.4f+7(7)8.5p+1(3)7	16.400673
30	4f¹²5s²5p³	4f+6(4)4.5p+1(3)5	16.824471
31	4f¹²5s²5p³	4f-5(5)5.4f+7(7)10.5p+1(3)9	16.857139
32	4f¹²5s²5p³	4f-5(5)5.4f+7(-7)10.5p+1(3)11	17.125132
33	4f¹²5s²5p³	4f+6(4)4.5p+1(3)3	17.421249
34	4f¹²5s²5p³	4f-5(5)5.4f+7(7)6.5p+1(3)7	17.509417
35	4f¹²5s²5p³	4f-5(5)5.4f+7(7)8.5p+1(3)11	17.527564
36	4f¹²5s²5p³	4f-5(5)5.4f+7(7)8.5p+1(3)9	17.779745
37	4f¹²5s²5p³	4f-4(8)8.5p+1(3)5	17.834973
38	4f¹²5s²5p³	4f+6(4)4.5p+1(3)1	17.891446
39	4f¹²5s²5p³	4f-5(5)5.4f+7(7)6.5p+1(3)5	18.053266
40	4f¹²5s²5p³	4f-5(5)5.4f+7(7)6.5p+1(3)7	18.202150
41	4f¹²5s²5p³	4f-5(5)5.4f+7(7)6.5p+1(3)9	18.356867
42	4f¹²5s²5p³	4f-5(5)5.4f+7(7)8.5p+1(3)7	18.596612
43	4f¹²5s²5p³	4f-5(5)5.4f+7(7)6.5p+1(3)3	19.061518
44	4f¹²5s²5p³	4f-5(5)5.4f+7(7)8.5p+1(3)5	19.422447
45	4f¹²5s²5p³	4f-4(8)8.5p+1(3)7	19.635564
46	4f¹²5s²5p³	4f-4(8)8.5p+1(3)11	19.732177
47	4f¹²5s²5p³	4f-4(8)8.5p+1(3)9	19.983774
48	4f¹²5s²5p³	4f-5(5)5.4f+7(7)4.5p+1(3)5	20.239222
49	4f¹²5s²5p³	4f-5(5)5.4f+7(7)12.5p+1(3)15	20.693116
50	4f¹²5s²5p³	4f-5(5)5.4f+7(7)4.5p+1(3)7	20.821427
51	4f¹²5s²5p³	4f+6(4)4.5p+1(3)1	20.856783
52	4f¹²5s²5p³	4f+6(4)4.5p+1(3)3	20.905069
53	4f¹²5s²5p³	4f-5(5)5.4f+7(7)12.5p+1(3)9	21.326702
54	4f¹²5s²5p³	4f+6(0)0.5p+1(3)3	21.575392
55	4f¹²5s²5p³	4f-5(5)5.4f+7(7)2.5p+1(3)5	22.169730
56	4f¹²5s²5p³	4f-5(5)5.4f+7(7)12.5p+1(3)11	22.498936
57	4f¹²5s²5p³	4f-5(5)5.4f+7(7)2.5p+1(3)1	22.737919
58	4f¹²5s²5p³	4f-5(5)5.4f+7(7)12.5p+1(3)13	22.989126
59	4f¹²5s²5p³	4f-4(4)4.5p+1(3)5	23.102462
60	4f¹²5s²5p³	4f-5(5)5.4f+7(7)2.5p+1(3)3	23.176613
61	4f¹²5s²5p³	4f-4(4)4.5p+1(3)7	23.443646
62	4f¹²5s²5p³	4f-5(5)5.4f+7(7)4.5p+1(3)3	23.652780
63	4f¹²5s²5p³	4f-4(4)4.5p+1(3)1	24.886345
64	4f¹²5s²5p³	4f+6(12)12.5p-1(1)11.5p+2(4)15	25.198660
65	4f¹³5s²5p²	4f+7(7)7.5p+2(4)11	25.225674
66	4f¹³5s²5p²	4f+7(7)7.5p+2(4)9	25.463906
67	4f¹³5s²5p²	4f+7(7)7.5p+2(4)7	25.560618
68	4f¹³5s²5p²	4f+7(7)7.5p+2(4)3	25.845469
69	4f¹²5s²5p³	4f+6(12)12.5p-1(1)11.5p+2(4)13	26.159966
70	4f¹³5s²5p²	4f+7(7)7.5p+2(4)5	26.641175
71	4f¹²5s²5p³	4f+6(8)8.5p-1(1)7.5p+2(4)11	26.677789
72	4f¹²5s²5p³	4f+6(12)12.5p-1(1)13.5p+2(4)9	26.929062
73	4f¹²5s²5p³	4f+6(12)12.5p-1(1)13.5p+2(4)11	27.017239
74	4f¹³5s²5p²	4f-5(5)5.5p+2(4)5	27.183576
75	4f¹²5s²5p³	4f+6(8)8.5p-1(1)9.5p+2(4)7	27.403642
76	4f¹³5s²5p²	4f-5(5)5.5p+2(4)3	27.583722
77	4f¹²5s²5p³	4f+6(8)8.5p-1(1)7.5p+2(4)9	27.737449
78	4f¹³5s²5p²	4f-5(5)5.5p+2(4)9	27.825543
79	4f¹³5s²5p²	4f-5(5)5.5p+2(4)1	27.843724
80	4f¹²5s²5p³	4f+6(8)8.5p-1(1)9.5p+2(4)5	28.013025
81	4f¹³5s²5p²	4f-5(5)5.5p+2(4)7	28.016205
82	4f¹²5s²5p³	4f+6(12)12.5p-1(1)13.5p+2(4)17	28.046730
83	4f¹²5s²5p³	4f-5(5)5.4f+7(7)10.5p-1(1)11.5p+2(4)9	28.073077
84	4f¹²5s²5p³	4f-5(5)5.4f+7(7)10.5p-1(1)11.5p+2(4)11	28.092883
85	4f¹²5s²5p³	4f-5(5)5.4f+7(7)10.5p-1(1)9.5p+2(4)13	28.093387
86	4f¹²5s²5p³	4f+6(12)12.5p-1(1)13.5p+2(4)15	28.284992
87	4f¹²5s²5p³	4f-5(5)5.4f+7(7)10.5p-1(1)11.5p+2(4)7	28.296631
88	4f¹²5s²5p³	4f+6(12)12.5p-1(1)13.5p+2(4)13	28.439835
89	4f¹²5s²5p³	4f-5(5)5.4f+7(7)8.5p-1(1)9.5p+2(4)7	28.636467
90	4f¹²5s²5p³	4f-5(5)5.4f+7(7)8.5p-1(1)9.5p+2(4)5	28.890217
91	4f¹²5s²5p³	4f-5(5)5.4f+7(7)6.5p-1(1)5.5p+2(4)9	29.031733
92	4f¹²5s²5p³	4f+6(8)8.5p-1(1)9.5p+2(4)13	29.106108
93	4f¹²5s²5p³	4f-5(5)5.4f+7(7)8.5p-1(1)7.5p+2(4)11	29.109282
94	4f¹²5s²5p³	4f+6(12)12.5p-1(1)11.5p+2(4)7	29.138058
95	4f¹²5s²5p³	4f-5(5)5.4f+7(7)6.5p-1(1)7.5p+2(4)5	29.247008
96	4f¹²5s²5p³	4f-5(5)5.4f+7(7)10.5p-1(1)11.5p+2(4)9	29.463518
97	4f¹²5s²5p³	4f-5(5)5.4f+7(7)6.5p-1(1)7.5p+2(4)3	29.510742
98	4f¹²5s²5p³	4f+6(4)4.5p-1(1)3.5p+2(4)7	29.581339
99	4f¹²5s²5p³	4f+6(8)8.5p-1(1)7.5p+2(4)3	29.660947
100	4f¹²5s²5p³	4f-5(5)5.4f+7(7)8.5p-1(1)7.5p+2(4)11	29.690268
101	4f¹²5s²5p³	4f+6(4)4.5p-1(1)5.5p+2(4)1	29.785016
102	4f¹²5s²5p³	4f-5(5)5.4f+7(7)6.5p-1(1)7.5p+2(4)7	29.802755
103	4f¹²5s²5p³	4f+6(8)8.5p-1(1)9.5p+2(4)11	29.835407
104	4f¹²5s²5p³	4f+6(12)12.5p-1(1)11.5p+2(4)9	29.935173
105	4f¹²5s²5p³	4f+6(8)8.5p-1(1)7.5p+2(4)9	29.992789
106	4f¹²5s²5p³	4f-4(8)8.5p-1(1)9.5p+2(4)5	30.135794
107	4f¹²5s²5p³	4f+6(8)8.5p-1(1)7.5p+2(4)7	30.208798
108	4f¹²5s²5p³	4f-4(0)0.5p+1(3)3	30.252252
109	4f¹²5s²5p³	4f-5(5)5.4f+7(7)10.5p-1(1)11.5p+2(4)15	30.315463
110	4f¹²5s²5p³	4f-5(5)5.4f+7(7)6.5p-1(1)7.5p+2(4)5	30.367034
111	4f¹²5s²5p³	4f-5(5)5.4f+7(7)10.5p-1(1)11.5p+2(4)13	30.420168
112	4f¹²5s²5p³	4f-4(8)8.5p-1(1)9.5p+2(4)5	30.515569
113	4f¹²5s²5p³	4f-5(5)5.4f+7(7)10.5p-1(1)9.5p+2(4)11	30.618863
114	4f¹²5s²5p³	4f-4(8)8.5p-1(1)9.5p+2(4)9	30.650657
115	4f¹²5s²5p³	4f+6(8)8.5p-1(1)7.5p+2(4)3	30.755836
116	4f¹²5s²5p³	4f-4(8)8.5p-1(1)9.5p+2(4)7	30.950833
117	4f¹³5s²5p²	4f+7(7)7.5p+2(0)7	31.028018
118	4f¹²5s²5p³	4f-5(5)5.4f+7(7)10.5p-1(1)9.5p+2(4)5	31.135297
119	4f¹²5s²5p³	4f-5(5)5.4f+7(7)8.5p-1(1)9.5p+2(4)13	31.239437
120	4f¹²5s²5p³	4f-5(5)5.4f+7(7)10.5p-1(1)9.5p+2(4)9	31.300041
121	4f¹²5s²5p³	4f+6(12)12.5p-1(1)11.5p+2(0)11	31.395345
122	4f¹²5s²5p³	4f-5(5)5.4f+7(7)6.5p-1(1)5.5p+2(4)1	31.455875
123	4f¹²5s²5p³	4f-4(8)8.5p-1(1)9.5p+2(4)11	31.524113
124	4f¹²5s²5p³	4f-5(5)5.4f+7(7)10.5p-1(1)9.5p+2(4)9	31.631040
125	4f¹²5s²5p³	4f+6(4)4.5p-1(1)5.5p+2(4)5	31.660101
126	4f¹²5s²5p³	4f-5(5)5.4f+7(7)10.5p-1(1)9.5p+2(4)7	31.690291
127	4f¹²5s²5p³	4f-5(5)5.4f+7(7)6.5p-1(1)7.5p+2(4)11	31.716101
128	4f¹²5s²5p³	4f-4(8)8.5p-1(1)9.5p+2(4)7	31.778531
129	4f¹²5s²5p³	4f-5(5)5.4f+7(7)8.5p-1(1)7.5p+2(4)3	31.849222
130	4f¹⁴5s¹5p²	5s+1(1)1	31.888981
131	4f¹²5s²5p³	4f-5(5)5.4f+7(7)8.5p-1(1)9.5p+2(4)11	32.085578
132	4f¹²5s²5p³	4f+6(4)4.5p-1(1)3.5p+2(4)1	32.085592
133	4f¹²5s²5p³	4f-5(5)5.4f+7(7)8.5p-1(1)7.5p+2(4)5	32.119796
134	4f¹²5s²5p³	4f+6(4)4.5p-1(1)3.5p+2(4)3	32.155819
135	4f¹²5s²5p³	4f-5(5)5.4f+7(7)10.5p-1(1)9.5p+2(4)7	32.172054
136	4f¹²5s²5p³	4f+6(4)4.5p-1(1)5.5p+2(4)9	32.219276
137	4f¹²5s²5p³	4f+6(12)12.5p-1(1)13.5p+2(0)13	32.250253
138	4f¹²5s²5p³	4f-5(5)5.4f+7(7)6.5p-1(1)5.5p+2(4)3	32.284567
139	4f¹²5s²5p³	4f-5(5)5.4f+7(7)6.5p-1(1)7.5p+2(4)9	32.310825
140	4f¹²5s²5p³	4f+6(4)4.5p-1(1)3.5p+2(4)5	32.430748
141	4f¹²5s²5p³	4f-4(8)8.5p-1(1)7.5p+2(4)7	32.599412
142	4f¹²5s²5p³	4f-5(5)5.4f+7(7)2.5p-1(1)1.5p+2(4)5	32.710532
143	4f¹²5s²5p³	4f+6(8)8.5p-1(1)9.5p+2(0)9	32.722893
144	4f¹²5s²5p³	4f-5(5)5.4f+7(7)6.5p-1(1)5.5p+2(4)3	32.726514
145	4f¹²5s²5p³	4f-4(8)8.5p-1(1)9.5p+2(4)13	32.788252
146	4f¹²5s²5p³	4f-5(5)5.4f+7(7)6.5p-1(1)7.5p+2(4)7	32.803691
147	4f¹³5s²5p²	4f-5(5)5.5p+2(0)5	33.190258
148	4f¹²5s²5p³	4f-5(5)5.4f+7(7)12.5p-1(1)13.5p+2(4)9	33.311662
149	4f¹²5s²5p³	4f-4(8)8.5p-1(1)9.5p+2(4)11	33.320945
150	4f¹²5s²5p³	4f-5(5)5.4f+7(7)12.5p-1(1)11.5p+2(4)15	33.356951
151	4f¹²5s²5p³	4f+6(8)8.5p-1(1)7.5p+2(0)7	33.409179
152	4f¹²5s²5p³	4f-4(8)8.5p-1(1)7.5p+2(4)3	33.506910
153	4f¹²5s²5p³	4f-4(8)8.5p-1(1)7.5p+2(4)5	33.541559
154	4f¹²5s²5p³	4f-4(4)4.5p-1(1)5.5p+2(4)1	33.637808
155	4f¹²5s²5p³	4f-5(5)5.4f+7(7)8.5p-1(1)7.5p+2(0)7	33.638887
156	4f¹²5s²5p³	4f-5(5)5.4f+7(7)12.5p-1(1)13.5p+2(4)11	33.703349
157	4f¹²5s²5p³	4f-5(5)5.4f+7(7)10.5p-1(1)9.5p+2(0)9	33.705428
158	4f¹²5s²5p³	4f-5(5)5.4f+7(7)8.5p-1(1)9.5p+2(0)9	33.869720
159	4f¹²5s²5p³	4f-4(8)8.5p-1(1)7.5p+2(4)3	33.944386
160	4f¹²5s²5p³	4f-4(8)8.5p-1(1)9.5p+2(4)13	34.004247
161	4f¹²5s²5p³	4f-4(8)8.5p-1(1)7.5p+2(4)3	34.099755
162	4f¹²5s²5p³	4f+6(4)4.5p-1(1)5.5p+2(0)5	34.102104
163	4f¹²5s²5p³	4f-5(5)5.4f+7(7)10.5p-1(1)11.5p+2(0)11	34.135950
164	4f¹²5s²5p³	4f-4(8)8.5p-1(1)7.5p+2(4)7	34.455709
165	4f¹²5s²5p³	4f-4(8)8.5p-1(1)7.5p+2(4)5	34.503115
166	4f¹²5s²5p³	4f-5(5)5.4f+7(7)4.5p-1(1)5.5p+2(4)1	34.566251
167	4f¹²5s²5p³	4f-5(5)5.4f+7(7)6.5p-1(1)7.5p+2(0)7	34.581228
168	4f¹²5s²5p³	4f-4(8)8.5p-1(1)7.5p+2(4)9	34.785497
169	4f¹²5s²5p³	4f-4(4)4.5p-1(1)5.5p+2(4)9	34.912240
170	4f¹²5s²5p³	4f-4(4)4.5p-1(1)3.5p+2(4)5	34.933144
171	4f¹²5s²5p³	4f-5(5)5.4f+7(7)4.5p-1(1)5.5p+2(4)3	35.233127
172	4f¹²5s²5p³	4f-5(5)5.4f+7(7)12.5p-1(1)11.5p+2(4)13	35.331629
173	4f¹²5s²5p³	4f-4(4)4.5p-1(1)5.5p+2(4)7	35.335261
174	4f¹²5s²5p³	4f-5(5)5.4f+7(7)2.5p-1(1)3.5p+2(4)1	35.353611
175	4f¹²5s²5p³	4f-4(8)8.5p-1(1)7.5p+2(4)5	35.358568
176	4f¹²5s²5p³	4f-5(5)5.4f+7(7)4.5p-1(1)3.5p+2(4)3	35.443479
177	4f¹²5s²5p³	4f-5(5)5.4f+7(7)12.5p-1(1)13.5p+2(4)17	35.506997
178	4f¹²5s²5p³	4f-5(5)5.4f+7(7)12.5p-1(1)11.5p+2(4)11	35.519342
179	4f¹²5s²5p³	4f-5(5)5.4f+7(7)12.5p-1(1)13.5p+2(4)15	35.687177
180	4f¹²5s²5p³	4f-5(5)5.4f+7(7)2.5p-1(1)3.5p+2(4)5	35.832089
181	4f¹²5s²5p³	4f-4(8)8.5p-1(1)9.5p+2(0)9	35.889007
182	4f¹²5s²5p³	4f-5(5)5.4f+7(7)8.5p-1(1)7.5p+2(0)7	35.953208
183	4f¹²5s²5p³	4f-4(4)4.5p-1(1)3.5p+2(4)1	36.137604
184	4f¹²5s²5p³	4f-5(5)5.4f+7(7)2.5p-1(1)3.5p+2(4)3	36.266912
185	4f¹²5s²5p³	4f-5(5)5.4f+7(7)6.5p-1(1)5.5p+2(0)5	36.417751
186	4f¹²5s²5p³	4f-5(5)5.4f+7(7)12.5p-1(1)11.5p+2(4)7	36.686838
187	4f¹²5s²5p³	4f-5(5)5.4f+7(7)12.5p-1(1)11.5p+2(4)9	36.981241
188	4f¹²5s²5p³	4f-5(5)5.4f+7(7)2.5p-1(1)1.5p+2(4)3	36.996846
189	4f¹²5s²5p³	4f+6(4)4.5p-1(1)5.5p+2(0)5	37.131836
190	4f¹²5s²5p³	4f-5(5)5.4f+7(7)4.5p-1(1)3.5p+2(4)1	37.136391
191	4f¹²5s²5p³	4f-5(5)5.4f+7(7)12.5p-1(1)11.5p+2(4)7	37.253204
192	4f¹²5s²5p³	4f-4(4)4.5p-1(1)3.5p+2(4)5	37.454373
193	4f¹²5s²5p³	4f-5(5)5.4f+7(7)2.5p-1(1)3.5p+2(4)7	37.610500
194	4f¹²5s²5p³	4f-4(4)4.5p-1(1)3.5p+2(4)3	37.748395
195	4f¹²5s²5p³	4f-4(4)4.5p-1(1)5.5p+2(4)9	37.811969
196	4f¹²5s²5p³	4f-4(8)8.5p-1(1)7.5p+2(0)7	38.345107
197	4f¹²5s²5p³	4f-5(5)5.4f+7(7)4.5p-1(1)3.5p+2(0)3	38.556955
198	4f¹²5s²5p³	4f-5(5)5.4f+7(7)2.5p-1(1)3.5p+2(4)5	38.846072
199	4f¹²5s²5p³	4f-5(5)5.4f+7(7)12.5p-1(1)13.5p+2(0)13	39.722163
200	4f¹³5s¹5p³	4f+7(7)7.5s+1(1)8.5p+1(3)11	39.977587
201	4f¹²5s²5p³	4f-5(5)5.4f+7(7)2.5p-1(1)1.5p+2(0)1	40.009869
202	4f¹³5s¹5p³	4f+6(0)0.5p-1(1)1.5p+2(0)1	40.143273
203	4f¹²5s²5p³	4f-4(4)4.5p-1(1)3.5p+2(0)3	40.319889
204	4f¹²5s²5p³	4f-5(5)5.4f+7(7)12.5p-1(1)11.5p+2(0)11	40.349004
205	4f¹⁴5s¹5p²	5s+1(1)1.5p-1(1)0.5p+1(3)3	40.558843
206	4f¹²5s²5p³	4f-5(5)5.4f+7(7)4.5p-1(1)5.5p+2(0)5	40.642163
207	4f¹³5s¹5p³	4f+7(7)7.5s+1(1)6.5p+1(3)5	40.988890
208	4f¹³5s¹5p³	4f+7(7)7.5s+1(1)8.5p+1(3)9	41.140485
209	4f¹³5s¹5p³	4f+7(7)7.5s+1(1)6.5p+1(3)7	41.198875
210	4f¹²5s²5p³	4f-5(5)5.4f+7(7)2.5p-1(1)3.5p+2(0)3	41.215262
211	4f¹³5s¹5p³	4f+7(7)7.5s+1(1)6.5p+1(3)3	41.408168
212	4f¹³5s¹5p³	4f-5(5)5.5s+1(1)4.5p+1(3)1	42.003775
213	4f¹²5s²5p³	4f+6(12)12.5p+3(3)13	43.025335
214	4f¹²5s²5p³	4f+6(12)12.5p+3(3)11	43.297322
215	4f¹²5s²5p³	4f-4(0)0.5p-1(1)1.5p+2(4)3	43.350760
216	4f¹³5s¹5p³	4f-5(5)5.5s+1(1)4.5p+1(3)3	43.392389
217	4f¹²5s²5p³	4f+6(12)12.5p+3(3)15	43.406285
218	4f¹⁴5s¹5p²	5s+1(1)1.5p-1(1)2.5p+1(3)5	43.608173
219	4f¹³5s¹5p³	4f-5(5)5.5s+1(1)6.5p+1(3)9	43.884680
220	4f¹²5s²5p³	4f+6(8)8.5p+3(3)9	44.013274
221	4f¹³5s¹5p³	4f-5(5)5.5s+1(1)4.5p+1(3)5	44.086014
222	4f¹²5s²5p³	4f+6(8)8.5p+3(3)11	44.238316
223	4f¹³5s¹5p³	4f-5(5)5.5s+1(1)6.5p+1(3)7	44.238615
224	4f¹²5s²5p³	4f-4(0)0.5p-1(1)1.5p+2(4)5	44.585410
225	4f¹²5s²5p³	4f+6(8)8.5p+3(3)5	45.006992
226	4f¹²5s²5p³	4f-5(5)5.4f+7(7)10.5p+3(3)11	45.017933
227	4f¹²5s²5p³	4f-5(5)5.4f+7(7)10.5p+3(3)9	45.045473
228	4f¹²5s²5p³	4f+6(8)8.5p+3(3)7	45.090392
229	4f¹²5s²5p³	4f-5(5)5.4f+7(7)8.5p+3(3)9	45.574024
230	4f¹²5s²5p³	4f-5(5)5.4f+7(7)10.5p+3(3)13	45.776380
231	4f¹²5s²5p³	4f-5(5)5.4f+7(7)8.5p+3(3)7	45.858203
232	4f¹²5s²5p³	4f-5(5)5.4f+7(7)10.5p+3(3)7	46.339124
233	4f¹²5s²5p³	4f+6(4)4.5p+3(3)1	46.446157
234	4f¹²5s²5p³	4f+6(12)12.5p+3(3)9	46.472647
235	4f¹²5s²5p³	4f-5(5)5.4f+7(7)6.5p+3(3)3	46.568953
236	4f¹³5s¹5p³	4f+7(7)7.5s+1(1)8.5p+1(3)5	46.616534
237	4f¹²5s²5p³	4f-5(5)5.4f+7(7)8.5p+3(3)5	46.666498
238	4f¹³5s¹5p³	4f+7(7)7.5s+1(1)6.5p+1(3)9	46.718090
239	4f¹²5s²5p³	4f-5(5)5.4f+7(7)6.5p+3(3)5	46.804436
240	4f¹²5s²5p³	4f-5(5)5.4f+7(7)8.5p+3(3)11	46.818182
241	4f¹²5s²5p³	4f+6(4)4.5p+3(3)3	46.867630
242	4f¹²5s²5p³	4f-5(5)5.4f+7(7)6.5p+3(3)9	46.897059
243	4f¹²5s²5p³	4f+6(4)4.5p+3(3)7	47.131872
244	4f¹²5s²5p³	4f-4(8)8.5p+3(3)7	47.498949
245	4f¹²5s²5p³	4f-4(0)0.5p-1(1)1.5p+2(0)1	47.601261
246	4f¹⁴5s¹5p²	5s+1(1)1.5p-1(1)2.5p+1(3)3	47.867842
247	4f¹³5s¹5p³	4f+7(7)7.5s+1(1)8.5p+1(3)7	47.963146
248	4f¹²5s²5p³	4f-5(5)5.4f+7(7)6.5p+3(3)7	48.284880
249	4f¹²5s²5p³	4f-4(8)8.5p+3(3)9	48.314230
250	4f¹²5s²5p³	4f-4(8)8.5p+3(3)11	48.357492
251	4f¹²5s²5p³	4f+6(4)4.5p+3(3)5	48.358299
252	4f¹²5s²5p³	4f-4(8)8.5p+3(3)5	48.625980
253	4f¹²5s²5p³	4f-5(5)5.4f+7(7)4.5p+3(3)1	48.890449
254	4f¹³5s¹5p³	4f-5(5)5.5s+1(1)6.5p+1(3)3	48.914054
255	4f¹²5s²5p³	4f-5(5)5.4f+7(7)12.5p+3(3)13	49.313778
256	4f¹³5s¹5p³	4f-5(5)5.5s+1(1)6.5p+1(3)7	49.571514
257	4f¹²5s²5p³	4f+6(4)4.5p+3(3)3	49.586195
258	4f¹²5s²5p³	4f-5(5)5.4f+7(7)4.5p+3(3)7	49.919408
259	4f¹²5s²5p³	4f-5(5)5.4f+7(7)12.5p+3(3)11	50.371537
260	4f¹⁴5s¹5p²	5s+1(1)1.5p-1(1)2.5p+1(3)1	50.452949
261	4f¹³5s¹5p³	4f-5(5)5.5s+1(1)6.5p+1(3)5	50.744707
262	4f¹²5s²5p³	4f-4(4)4.5p+3(3)1	50.746650
263	4f¹²5s²5p³	4f-4(4)4.5p+3(3)3	50.893695
264	4f¹²5s²5p³	4f+6(4)4.5p+3(3)5	50.970529
265	4f¹³5s¹5p³	4f+7(7)7.5s+1(1)8.5p-1(1)7.5p+2(4)11	51.131667
266	4f¹²5s²5p³	4f-5(5)5.4f+7(7)12.5p+3(3)15	51.788425
267	4f¹²5s²5p³	4f-4(4)4.5p+3(3)7	51.985278
268	4f¹²5s²5p³	4f-5(5)5.4f+7(7)2.5p+3(3)5	52.093916
269	4f¹³5s¹5p³	4f+7(7)7.5s+1(1)8.5p-1(1)7.5p+2(4)9	52.398490
270	4f¹²5s²5p³	4f+6(0)0.5p+3(3)3	52.440969
271	4f¹³5s¹5p³	4f+7(7)7.5s+1(1)6.5p-1(1)7.5p+2(4)3	52.516271
272	4f¹³5s¹5p³	4f+7(7)7.5s+1(1)6.5p-1(1)7.5p+2(4)7	52.871630
273	4f¹³5s¹5p³	4f+7(7)7.5s+1(1)6.5p-1(1)7.5p+2(4)5	52.967365
274	4f¹³5s¹5p³	4f-5(5)5.5s+1(1)4.5p-1(1)5.5p+2(4)1	53.136186
275	4f¹²5s²5p³	4f-5(5)5.4f+7(7)12.5p+3(3)9	53.148205
276	4f¹²5s²5p³	4f-5(5)5.4f+7(7)4.5p+3(3)3	53.432744
277	4f¹²5s²5p³	4f-4(4)4.5p+3(3)5	53.482487
278	4f¹³5s¹5p³	4f-5(5)5.5s+1(1)4.5p-1(1)5.5p+2(4)3	53.556245
279	4f¹³5s¹5p³	4f-5(5)5.5s+1(1)4.5p-1(1)5.5p+2(4)5	54.072377
280	4f¹²5s²5p³	4f-5(5)5.4f+7(7)2.5p+3(3)1	54.212902
281	4f¹⁴5s¹5p²	5s+1(1)1.5p+2(4)5	54.710411
282	4f¹³5s¹5p³	4f-5(5)5.5s+1(1)6.5p-1(1)5.5p+2(4)9	54.778699
283	4f¹³5s¹5p³	4f+7(7)7.5s+1(1)8.5p-1(1)9.5p+2(4)13	55.063904
284	4f¹³5s¹5p³	4f+7(7)7.5s+1(1)8.5p-1(1)9.5p+2(4)11	55.118007
285	4f¹³5s¹5p³	4f-5(5)5.5s+1(1)4.5p-1(1)5.5p+2(4)7	55.233560
286	4f¹³5s¹5p³	4f+7(7)7.5s+1(1)6.5p-1(1)7.5p+2(4)9	55.423570
287	4f¹³5s¹5p³	4f+7(7)7.5s+1(1)6.5p-1(1)7.5p+2(4)7	55.687604
288	4f¹³5s¹5p³	4f+7(7)7.5s+1(1)6.5p-1(1)5.5p+2(4)1	56.090306
289	4f¹³5s¹5p³	4f+7(7)7.5s+1(1)6.5p-1(1)5.5p+2(4)3	56.104775
290	4f¹⁴5s¹5p²	5s+1(1)1.5p+2(4)5	57.091806
291	4f¹³5s¹5p³	4f-5(5)5.5s+1(1)6.5p-1(1)7.5p+2(4)11	57.767247
292	4f¹³5s¹5p³	4f-5(5)5.5s+1(1)6.5p-1(1)5.5p+2(4)7	58.051208
293	4f¹³5s¹5p³	4f-5(5)5.5s+1(1)4.5p-1(1)3.5p+2(4)3	58.085215
294	4f¹³5s¹5p³	4f-5(5)5.5s+1(1)4.5p-1(1)5.5p+2(4)9	58.102775
295	4f¹³5s¹5p³	4f-5(5)5.5s+1(1)4.5p-1(1)3.5p+2(4)5	58.108579
296	4f¹³5s¹5p³	4f-5(5)5.5s+1(1)4.5p-1(1)3.5p+2(4)1	58.157443
297	4f¹³5s¹5p³	4f+7(7)7.5s+1(1)8.5p-1(1)7.5p+2(0)7	58.332193
298	4f¹³5s²5p¹5d¹	4f+7(7)7.5p-1(1)6.5d-1(3)3	58.415197
299	4f¹³5s²5p¹5d¹	4f+7(7)7.5p-1(1)8.5d-1(3)9	58.772385
300	4f¹³5s²5p¹5d¹	4f+7(7)7.5p-1(1)6.5d-1(3)5	58.867240
301	4f¹³5s²5p¹5d¹	4f+7(7)7.5p-1(1)8.5d-1(3)11	59.062629
302	4f¹³5s²5p¹5d¹	4f+7(7)7.5p-1(1)6.5d-1(3)7	59.176646
303	4f¹³5s¹5p³	4f+7(7)7.5s+1(1)6.5p-1(1)7.5p+2(0)7	59.486179
304	4f¹²5s²5p³	4f-4(0)0.5p+3(3)3	59.792970

Table 2. Comparison of calculated wavelengths (in nm) using FAC with other wavelengths for various transitions in Eu-like W. i and j represent the sequential numbers assigned in Table 1 to the lower and upper levels, respectively.

Transition	i	j	Our Work	Experimental ¹	Other Theory ¹
{[(4f¹³)_5/25s]₃(5p²_1/25p_3/2)_3/2}_3/2→{[(4f ¹³)_5/25s²]_5/2(5p²_1/2)₀}_5/2	2	278	24.349	24.623 ± 0.012	25.084
{[(4f¹³)_5/25s]₂(5p²_1/25p_3/2)_3/2}_7/2→{[(4f ¹³)_5/25s²]_5/2(5p²_1/2)₀}_5/2	2	256	26.416	25.225 ± 0.018	25.746
{[(4f¹³)_5/25s]₃(5p²_1/25p_3/2)_3/2}_5/2→{[(4f ¹³)_5/25s²]_5/2(5p²_1/2)₀}_5/2	2	261	25.772	25.409 ± 0.017	26.198

¹ Reference [30].

Table 3. Oscillator strengths (length and velocity form) gf_L and gf_v, vacuum wavelengths λ (in nm), and transition probabilities A_ji (in s⁻¹) for some strong electric dipole (E1) transitions from the ground state to various levels of Eu-like W.

j	λ (nm)	gf_L	gf_v	A_ji
207	30.2482	1.532E-02	1.181E-02	1.861E+08
209	30.0941	1.647E-02	1.400E-02	1.516E+08
219	28.2523	6.616E-02	6.040E-02	5.529E+08
223	28.0262	1.887E-02	1.607E-02	2.003E+08
236	26.5966	8.246E-01	6.311E-01	1.296E+10
238	26.5388	1.685E+00	1.322E+00	1.596E+10
247	25.8499	1.118E+00	8.577E-01	1.395E+10
256	25.0112	3.056E-01	2.369E-01	4.073E+09
282	22.6337	1.033E-02	1.017E-02	1.345E+08
297	21.2548	3.173E-02	4.308E-02	5.857E+08

Table 4. Oscillator strengths gf_ij, vacuum wavelengths λ (in nm), and transition probabilities A_ji (in s⁻¹) for magnetic dipole (M1) transitions from the ground state calculated for Eu-like W.

J	λ (nm)	gf_ij	A_ji(s⁻¹)
2	470.3942	3.751E-06	1.885E+02
3	119.1397	1.653E-05	7.768E+03
4	109.3488	9.150E-06	8.507E+03
6	103.4700	1.244E-05	9.688E+03
9	98.4066	2.064E-07	2.369E+02
10	96.1341	2.104E-06	1.519E+03
11	95.4681	1.038E-06	9.496E+02
13	89.1730	2.619E-08	2.746E+01
14	87.7895	5.872E-07	8.470E+02
16	84.7958	2.574E-09	2.388E+00
19	84.0012	4.295E-08	4.060E+01
20	82.2056	1.588E-07	1.959E+02
21	80.5164	1.239E-07	1.275E+02
23	79.9458	3.759E-10	6.538E-01
25	78.1530	9.817E-09	1.340E+01
28	76.7914	1.085E-08	2.045E+01
29	75.5970	1.530E-07	2.232E+02
30	73.6928	1.854E-08	3.795E+01
31	73.5500	5.146E-08	6.345E+01
34	70.8100	8.218E-10	1.367E+00
36	69.7334	6.906E-09	9.473E+00
37	69.5175	1.369E-08	3.149E+01
39	68.6769	3.374E-10	7.953E-01
40	68.1151	2.651E-11	4.764E-02
41	67.5410	1.421E-09	2.078E+00
42	66.6703	2.688E-08	5.042E+01
44	63.8355	6.616E-09	1.805E+01
45	63.1427	1.790E-08	3.743E+01
47	62.0424	2.034E-09	3.525E+00
48	61.2594	4.736E-10	1.403E+00
50	59.5464	1.348E-09	3.170E+00
53	58.1357	1.264E-08	2.495E+01
55	55.9250	1.177E-09	4.184E+00
59	53.6671	5.867E-10	2.265E+00
61	52.8860	1.829E-11	5.452E-02
66	48.6902	2.296E-09	6.460E+00
75	45.2437	7.166E-10	2.919E+00
80	44.2595	2.668E-10	1.514E+00
81	44.2545	3.462E-10	1.474E+00
83	44.1648	7.762E-09	2.654E+01
87	43.8159	6.396E-09	2.778E+01
89	43.2959	2.130E-09	9.474E+00
90	42.9156	8.688E-10	5.244E+00
91	42.7064	6.188E-09	2.263E+01
94	42.5506	5.833E-09	2.686E+01
95	42.3921	1.434E-11	8.871E-02
96	42.0806	5.565E-09	2.096E+01
98	41.9130	1.867E-09	8.861E+00
102	41.6016	2.435E-09	1.173E+01
104	41.4176	8.900E-09	3.461E+01
105	41.3380	1.757E-09	6.858E+00
106	41.1418	2.075E-09	1.363E+01
107	41.0424	4.872E-09	2.412E+01
110	40.8286	1.550E-11	1.034E-01
112	40.6298	1.542E-09	1.038E+01
114	40.4507	2.878E-10	1.173E+00
116	40.0584	1.399E-10	7.269E-01
118	39.8211	3.407E-09	2.389E+01
120	39.6115	1.780E-08	7.567E+01
124	39.1970	3.920E-09	1.702E+01
125	39.1610	7.961E-09	5.771E+01
126	39.1237	1.382E-10	7.528E-01
128	39.0151	2.709E-09	1.484E+01
133	38.6006	6.222E-09	4.642E+01
135	38.5379	6.191E-11	3.476E-01
139	38.3723	2.555E-09	1.157E+01
140	38.2304	6.538E-10	4.973E+00
141	38.0327	1.381E-09	7.960E+00
142	37.9035	3.474E-09	2.688E+01
143	37.8891	2.346E-09	1.090E+01
146	37.7958	2.487E-10	1.452E+00
147	37.3556	6.913E-09	5.508E+01
148	37.2195	5.742E-10	2.765E+00
153	36.9644	3.356E-10	2.731E+00
155	36.8574	5.074E-10	3.114E+00
157	36.7846	1.956E-09	9.642E+00
158	36.6062	8.529E-10	4.246E+00
164	35.9836	4.992E-11	3.215E-01
165	35.9342	1.351E-10	1.163E+00
167	35.8530	1.308E-10	8.484E-01
168	35.6425	2.604E-10	1.367E+00
169	35.5131	1.517E-10	8.025E-01
170	35.4919	2.602E-09	2.296E+01
173	35.0880	2.364E-09	1.601E+01
180	34.6014	1.203E-09	1.117E+01
181	34.5466	2.024E-09	1.131E+01
182	34.4849	2.403E-09	1.685E+01
185	34.0450	1.289E-09	1.236E+01
186	33.7953	3.482E-09	2.542E+01
187	33.5262	5.150E-09	3.056E+01
189	33.3903	2.300E-10	2.293E+00
191	33.2815	1.441E-08	1.085E+02
192	33.1027	1.192E-10	1.209E+00
193	32.9653	2.964E-11	2.274E-01
195	32.7897	7.813E-10	4.847E+00
196	32.3338	4.930E-10	3.932E+00
198	31.9168	1.226E-10	1.338E+00
206	30.5063	1.277E-10	1.525E+00
225	27.5478	7.954E-11	1.165E+00
231	27.0364	5.195E-11	5.926E-01
232	26.7558	1.034E-10	1.204E+00
234	26.6790	5.105E-11	4.784E-01
237	26.5681	9.262E-12	1.459E-01
239	26.4898	3.333E-11	5.280E-01
242	26.4375	3.896E-11	3.718E-01
243	26.3058	7.933E-11	9.558E-01
248	25.6776	8.008E-11	1.013E+00
249	25.6620	2.285E-11	2.314E-01
251	25.6387	1.583E-11	2.677E-01
258	24.8369	2.726E-11	3.685E-01
267	23.8499	9.560E-11	1.401E+00
268	23.8001	2.857E-11	5.607E-01
275	23.3280	1.146E-10	1.405E+00

Table 5. Oscillator strengths gf_ij, vacuum wavelengths λ (in nm), and transition probabilities A_ji (in s⁻¹) for magnetic quadrupole (M2) transitions from the ground state in Eu-like W.

j	λ (nm)	gf_ij	A_ji (s⁻¹)
200	31.0134	4.147E-09	2.397E+01
205	30.5690	3.013E-10	5.377E+00
207	30.2482	1.820E-09	2.211E+01
208	30.1368	3.279E-09	2.408E+01
209	30.0941	2.665E-09	2.454E+01
211	29.9420	8.454E-10	1.572E+01
216	28.5728	5.206E-10	1.063E+01
218	28.4314	6.824E-11	9.385E-01
219	28.2523	3.457E-10	2.889E+00
221	28.1233	4.822E-10	6.778E+00
223	28.0262	3.373E-10	3.580E+00
236	26.5966	5.529E-12	8.689E-02
238	26.5388	2.201E-13	2.084E-03
246	25.9014	6.804E-11	1.691E+00
247	25.8499	1.913E-11	2.387E-01
254	25.3474	7.382E-12	1.916E-01
256	25.0112	8.935E-12	1.191E-01
261	24.4329	6.642E-13	1.237E-02
265	24.2480	1.490E-09	1.409E+01
269	23.6618	1.444E-09	1.720E+01
271	23.6087	5.501E-10	1.646E+01
272	23.4500	9.282E-10	1.407E+01
273	23.4077	7.612E-10	1.544E+01
278	23.1503	9.312E-12	2.897E-01
279	22.9293	4.199E-11	8.879E-01
281	22.6619	5.448E-11	1.179E+00
284	22.4943	1.238E-11	1.360E-01
285	22.4473	1.773E-10	2.934E+00
286	22.3703	1.152E-11	1.536E-01
287	22.2642	4.283E-11	7.204E-01
289	22.0987	5.163E-13	1.763E-02
290	21.7166	5.489E-12	1.294E-01
291	21.4627	6.646E-12	8.020E-02
292	21.3577	4.977E-12	9.097E-02
294	21.3388	1.916E-12	2.807E-02
295	21.3366	2.720E-12	6.642E-02
297	21.2549	7.816E-11	1.443E+00
298	21.2246	3.513E-11	1.300E+00
299	21.0957	3.285E-11	4.924E-01
300	21.0617	4.574E-12	1.146E-01
301	20.9920	2.376E-11	2.997E-01
302	20.9515	1.754E-11	3.332E-01
303	20.8425	3.451E-12	6.624E-02

Table 6. Collisional excitation cross-sections (100 Mb) of Eu-like W from the ground state to various levels.

Energy (eV) /Transition	0–3	0–4	0–5	Energy (eV) /Transition	0–1	Energy (eV) /Transition	0–2	Energy (eV) /Transition	0–29
4.47E-01	2.63E+02	1.07E+02	1.79E+02	1.61E-01	3.14E+02	1.11E-01	2.73E+03	6.30E-01	8.61E+00
1.42E+01	1.03E+02	4.29E+01	8.40E+01	6.82E+00	8.81E+01	5.37E+00	9.22E+02	1.74E+01	4.29E+00
4.80E+01	3.40E+01	1.34E+01	3.68E+01	2.65E+01	2.55E+01	2.24E+01	2.79E+02	5.51E+01	1.98E+00
1.31E+02	9.42E+00	3.14E+00	1.61E+01	8.48E+01	6.25E+00	7.77E+01	7.50E+01	1.40E+02	8.90E-01
3.30E+02	2.60E+00	5.62E-01	7.06E+00	2.55E+02	1.08E+00	2.54E+02	1.49E+01	3.28E+02	4.06E-01
7.95E+02	8.12E-01	7.11E-02	3.01E+00	7.34E+02	2.30E-01	7.95E+02	1.60E+00	7.34E+02	1.83E-01
Energy (eV) /Transition	0–6	0–7	0–8	0–9	0–10	0–11	0–13	0–14	0–16
8.77E-01	1.65E+02	4.82E+01	7.03E+02	2.79E+02	1.39E+02	3.13E+02	8.94E+00	9.00E+00	2.89E+01
2.22E+01	5.29E+01	1.85E+01	2.70E+02	1.08E+02	4.93E+01	1.23E+02	3.93E+00	3.03E+00	1.21E+01
6.79E+01	1.78E+01	8.14E+00	1.18E+02	4.74E+01	1.80E+01	5.50E+01	2.12E+00	9.23E-01	5.35E+00
1.66E+02	6.34E+00	3.86E+00	5.57E+01	2.23E+01	6.60E+00	2.67E+01	1.30E+00	2.44E-01	2.47E+00
3.72E+02	2.59E+00	1.87E+00	2.69E+01	1.08E+01	2.63E+00	1.34E+01	7.94E-01	5.98E-02	1.18E+00
7.95E+02	1.22E+00	8.94E-01	1.28E+01	5.10E+00	1.12E+00	6.67E+00	4.56E-01	1.47E-02	5.62E-01
Energy (eV) /Transition	0–18	0–22	0–24	Energy (eV) /Transition	0–12	0–15	0–17	0–19	0–20
8.77E-01	1.27E+00	6.97E+01	8.56E+00	6.08E-01	7.78E+01	3.22E+02	5.48E+01	5.88E+01	3.03E+01
2.22E+01	4.80E-01	3.06E+01	3.56E+00	2.14E+01	2.64E+01	1.35E+02	2.01E+01	2.25E+01	1.29E+01
6.79E+01	1.73E-01	1.40E+01	1.48E+00	7.59E+01	6.78E+00	5.42E+01	5.67E+00	6.98E+00	5.09E+00
1.66E+02	5.76E-02	6.64E+00	6.19E-01	2.17E+02	1.06E+00	2.19E+01	1.15E+00	1.78E+00	2.07E+00
3.72E+02	1.95E-02	3.21E+00	2.71E-01	5.74E+02	1.37E-01	8.93E+00	2.86E-01	5.32E-01	9.19E-01
7.95E+02	7.33E-03	1.54E+00	1.21E-01	1.43E+03	2.02E-02	3.60E+00	1.06E-01	1.93E-01	3.78E-01
Energy (eV) /Transition	0–21	0–23	0–25	0–26	0–27	Energy (eV) /Transition	0–28	0–30	0–31
6.08E-01	5.35E+02	9.02E+01	5.04E+02	2.71E+01	7.70E+01	1.22E+00	7.15E+01	6.76E+01	2.60E+02
2.14E+01	2.39E+02	3.80E+01	2.41E+02	1.08E+01	3.43E+01	3.42E+01	2.51E+01	2.38E+01	9.53E+01
7.59E+01	1.02E+02	1.44E+01	1.19E+02	3.54E+00	1.41E+01	1.09E+02	1.04E+01	9.56E+00	4.08E+01
2.17E+02	4.34E+01	5.40E+00	6.74E+01	1.11E+00	5.69E+00	2.78E+02	4.95E+00	4.14E+00	1.88E+01
5.74E+02	1.81E+01	2.15E+00	3.88E+01	4.41E-01	2.32E+00	6.50E+02	2.52E+00	1.86E+00	8.68E+00
1.43E+03	7.33E+00	8.78E-01	1.71E+01	1.99E-01	9.37E-01	1.43E+03	1.22E+00	8.44E-01	4.00E+00
Energy (eV) /Transition	0–28	0–30	0–31	0–32	0–33	0–34	0–35	0–36	0–37
1.22E+00	7.15E+01	6.76E+01	2.60E+02	6.66E+01	7.88E+01	8.88E+01	2.09E+01	4.37E+01	1.34E+02
3.42E+01	2.51E+01	2.38E+01	9.53E+01	2.34E+01	2.94E+01	3.23E+01	6.37E+00	1.53E+01	5.09E+01
1.09E+02	1.04E+01	9.56E+00	4.08E+01	9.30E+00	1.26E+01	1.34E+01	1.94E+00	5.94E+00	2.21E+01
2.78E+02	4.95E+00	4.14E+00	1.88E+01	4.05E+00	5.73E+00	6.11E+00	6.65E-01	2.52E+00	1.02E+01
6.50E+02	2.52E+00	1.86E+00	8.68E+00	1.84E+00	2.62E+00	2.88E+00	2.94E-01	1.14E+00	4.74E+00
1.43E+03	1.22E+00	8.44E-01	4.00E+00	8.46E-01	1.20E+00	1.35E+00	1.46E-01	5.23E-01	2.18E+00
Energy (eV) /Transition	0–38	0–39	0–40	0–41	0–42	0–43	0–44	0–45	0–46
1.22E+00	4.06E+00	3.24E+01	4.00E+01	2.40E+01	4.00E+01	2.37E+01	7.58E+00	2.61E+00	2.05E+00
3.42E+01	1.17E+00	1.17E+01	1.59E+01	8.06E+00	1.58E+01	9.02E+00	2.33E+00	9.78E-01	7.32E-01
1.09E+02	2.81E-01	4.61E+00	7.79E+00	2.85E+00	7.52E+00	3.76E+00	5.88E-01	4.14E-01	2.70E-01
2.78E+02	4.71E-02	1.98E+00	4.75E+00	1.12E+00	4.40E+00	1.68E+00	1.05E-01	2.24E-01	1.08E-01
6.50E+02	8.72E-03	8.87E-01	2.98E+00	5.00E-01	2.70E+00	7.70E-01	2.10E-02	1.42E-01	4.79E-02
1.43E+03	2.32E-03	4.05E-01	1.61E+00	2.36E-01	1.44E+00	3.54E-01	5.58E-03	7.83E-02	2.21E-02
Energy (eV) /Transition	0–47	0–48	0–49	0–50
1.22E+00	1.27E+01	9.06E+00	2.66E+01	1.08E+01
3.42E+01	4.46E+00	3.00E+00	8.92E+00	3.48E+00
1.09E+02	1.51E+00	9.06E-01	2.87E+00	9.59E-01
2.78E+02	5.11E-01	2.70E-01	1.02E+00	2.37E-01
6.50E+02	2.04E-01	1.03E-01	4.61E-01	7.70E-02
1.43E+03	8.86E-02	4.63E-02	2.30E-01	3.09E-02

Table 7. Configurations included in the different inputs with the number of fine structure levels for Pm-like W.

	INP1	INP2	INP3	INPF
Configuration	4f¹⁴5s, 4f¹³5s², 4f¹³5s5p, 4f¹⁴5p, 4f¹³5p²	4f¹⁴5s, 4f¹³5s², 4f¹³5s5p, 4f¹⁴5p, 4f¹³5p², 4f¹²5s²5p, 4f¹²5s5p², 4f¹²5p³	4f¹⁴5s, 4f¹³5s², 4f¹³5s5p, 4f¹⁴5p, 4f¹³5p², 4f¹²5s²5p, 4f¹²5s5p², 4f¹²5p³, 4f¹¹5s²5p², 4f¹¹5s5p³, 4f¹⁰5s²5p³, 4f¹⁰5s5p⁴	4f¹⁴5s, 4f¹³5s², 4f¹³5s5p, 4f¹⁴5p, 4f¹³5p², 4f¹²5s²5p, 4f¹²5s5p², 4f¹²5p³, 4f¹¹5s²5p², 4f¹¹5s5p³, 4f¹⁰5s²5p³, 4f¹⁰5s5p⁴, 4f¹²5s²5d, 4f¹²5s5d², 4f¹³5d², 4f¹³5p5d, 4f¹³5d², 4f¹³5p5d, 4f¹²5p5d², 4f¹²5p²5d, 4f¹³5s5d
Levels	59	680	7790	13,160
Ground state	4f¹³5s^{2 2}F_7/2	4f¹³5s^{2 2}F_7/2	4f¹³5s^{2 2}F_7/2	4f¹³5s^{2 2}F_7/2

Table 8. List of configurations included and the number of fine-structure levels arising from each configuration of Pm-like W.

Configuration	Total
4f¹⁴5s¹	1
4f¹³5s²	2
4f¹³5s¹ 5p¹	24
4f¹⁴5p¹	2
4f¹³5p²	36
4f¹²5s²5p¹	69
4f¹²5s¹5p²	335
4f¹²5p³	231
4f¹¹5s²5p²	594
4f¹¹5s¹5p³	1542
4f¹⁰5s²5p³	1971
4f¹⁰5s¹5p⁴	2947
4f¹²5s²5d¹	139
4f¹²5s¹5d²	910
4f¹³5d²	82
4f¹³5p¹5d¹	121
4f¹²5p¹5d²	2617
4f¹²5p²5d¹	1499
4f¹³5s¹5d¹	38

Table 9. Energy values (in eV) from each input for the 4f¹³5s5p configuration of Pm-like W.

S. No.	Level Index	2J	out1	out2	out3	outF
1	69	4f+7(7)7.5s+1(1)8.5p-1(1)7	28.34084	28.23032	28.33804	28.05699
2	85	4f+7(7)7.5s+1(1)6.5p-1(1)7	30.49845	30.39207	30.49463	30.07793
3	89	4f-5(5)5.5s+1(1)4.5p-1(1)5	30.51904	30.42783	30.53146	30.24463
4	91	4f+7(7)7.5s+1(1)8.5p-1(1)9	30.93588	30.81385	30.91735	30.53786
5	94	4f+7(7)7.5s+1(1)6.5p-1(1)5	31.59384	31.48818	31.59510	31.22191
6	108	4f-5(5)5.5s+1(1)6.5p-1(1)5	33.51591	33.39925	33.48623	33.07156
7	110	4f-5(5)5.5s+1(1)6.5p-1(1)7	33.59234	33.50230	33.60730	33.22125
8	114	4f-5(5)5.5s+1(1)4.5p-1(1)3	33.94001	33.79424	33.89133	33.52918
9	222	4f+7(7)7.5s+1(1)8.5p+1(3)11	42.28670	42.17790	42.21274	41.88907
10	250	4f+7(7)7.5s+1(1)6.5p+1(3)3	43.33967	43.16711	43.21708	42.84671
11	263	4f+7(7)7.5s+1(1)6.5p+1(3)5	43.69655	43.48007	43.54132	43.20679
12	266	4f-5(5)5.5s+1(1)4.5p+1(3)1	43.73023	43.55966	43.63034	43.25833
13	277	4f+7(7)7.5s+1(1)6.5p+1(3)7	44.14760	43.88220	43.94818	43.64971
14	279	4f+7(7)7.5s+1(1)8.5p+1(3)9	44.15898	43.88693	43.95022	43.67102
15	317	4f-5(5)5.5s+1(1)4.5p+1(3)3	45.52535	45.30258	45.36262	45.02438
16	326	4f-5(5)5.5s+1(1)6.5p+1(3)9	45.65222	45.44028	45.52273	45.17111
17	351	4f-5(5)5.5s+1(1)4.5p+1(3)5	46.47208	46.22915	46.29386	45.99735
18	357	4f-5(5)5.5s+1(1)6.5p+1(3)7	46.61544	46.37682	46.44845	46.14563
19	433	4f+7(7)7.5s+1(1)8.5p+1(3)5	51.21205	50.85405	50.89800	49.88168
20	434	4f+7(7)7.5s+1(1)6.5p+1(3)9	51.31237	50.99615	51.05140	49.98717
21	451	4f+7(7)7.5s+1(1)8.5p+1(3)7	52.80963	52.14431	52.20551	51.07045
22	460	4f-5(5)5.5s+1(1)6.5p+1(3)3	53.12149	52.74996	52.80752	51.79452
23	475	4f-5(5)5.5s+1(1)4.5p+1(3)7	53.89587	53.42507	53.48859	52.41451
24	493	4f-5(5)5.5s+1(1)6.5p+1(3)5	55.31426	54.63896	54.70557	53.48189

Table 10. Energy levels (in eV) for the lowest 500 levels calculated with FAC using INPF configurations for Pm-like W.

Level No.	Configuration	2J	FAC
0	4f¹³5s²	4f+7(7)7	0.000000
1	4f¹³5s²	4f-5(5)5	2.255395
2	4f¹²5s²5p¹	4f+6(12)12.5p-1(1)11	7.276828
3	4f¹²5s²5p¹	4f+6(12)12.5p-1(1)13	8.000018
4	4f¹²5s²5p¹	4f+6(8)8.5p-1(1)7	8.504221
5	4f¹²5s²5p¹	4f+6(8)8.5p-1(1)9	8.898153
6	4f¹²5s²5p¹	4f-5(5)5.4f+7(7)10.5p-1(1)11	9.837877
7	4f¹²5s²5p¹	4f-5(5)5.4f+7(7)10.5p-1(1)9	9.857320
8	4f¹²5s²5p¹	4f-5(5)5.4f+7(7)8.5p-1(1)7	10.537519
9	4f¹²5s²5p¹	4f-5(5)5.4f+7(7)6.5p-1(1)5	10.821138
10	4f¹²5s²5p¹	4f+6(4)4.5p-1(1)3	10.938403
11	4f¹²5s²5p¹	4f-5(5)5.4f+7(7)8.5p-1(1)9	11.036302
12	4f¹²5s²5p¹	4f-5(5)5.4f+7(7)6.5p-1(1)5	11.306358
13	4f¹²5s²5p¹	4f-5(5)5.4f+7(7)6.5p-1(1)7	11.775166
14	4f¹²5s²5p¹	4f-4(8)8.5p-1(1)9	12.546322
15	4f¹²5s²5p¹	4f-5(5)5.4f+7(7)4.5p-1(1)3	13.724712
16	4f¹²5s²5p¹	4f-4(8)8.5p-1(1)7	13.755493
17	4f¹²5s²5p¹	4f-4(4)4.5p-1(1)5	13.957189
18	4f¹²5s²5p¹	4f-5(5)5.4f+7(7)12.5p-1(1)13	14.902679
19	4f¹²5s²5p¹	4f-5(5)5.4f+7(7)2.5p-1(1)1	15.077341
20	4f¹²5s²5p¹	4f+6(0)0.5p-1(1)1	15.148716
21	4f¹²5s²5p¹	4f-5(5)5.4f+7(7)12.5p-1(1)11	15.246453
22	4f¹²5s²5p¹	4f-5(5)5.4f+7(7)2.5p-1(1)3	16.064828
23	4f¹²5s²5p¹	4f-4(4)4.5p-1(1)5	16.335222
24	4f¹²5s²5p¹	4f-4(4)4.5p-1(1)3	16.845319
25	4f¹¹5s²5p²	4f+5(15)15	20.958997
26	4f¹²5s²5p¹	4f+6(12)12.5p+1(3)15	21.711928
27	4f¹²5s²5p¹	4f+6(12)12.5p+1(3)11	22.687480
28	4f¹²5s²5p¹	4f+6(12)12.5p+1(3)9	22.793061
29	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)13	23.259954
30	4f¹²5s²5p¹	4f-4(0)0.5p-1(1)1	23.263519
31	4f¹²5s²5p¹	4f+6(12)12.5p+1(3)13	23.414228
32	4f¹²5s²5p¹	4f+6(8)8.5p+1(3)9	23.475916
33	4f¹²5s²5p¹	4f-5(5)5.4f+7(7)10.5p+1(3)7	23.595130
34	4f¹¹5s²5p²	4f+5(9)9	23.615822
35	4f¹¹5s²5p²	4f+5(11)11	23.666002
36	4f¹²5s²5p¹	4f+6(8)8.5p+1(3)5	23.951175
37	4f¹²5s²5p¹	4f+6(8)8.5p+1(3)11	24.192841
38	4f¹²5s²5p¹	4f-5(5)5.4f+7(7)10.5p+1(3)13	24.205246
39	4f¹²5s²5p¹	4f+6(8)8.5p+1(3)7	24.241919
40	4f¹¹5s²5p²	4f+5(3)3	24.903151
41	4f¹²5s²5p¹	4f-5(5)5.4f+7(7)10.5p+1(3)9	25.000189
42	4f¹²5s²5p¹	4f+6(8)8.5p+1(3)5	25.137622
43	4f¹⁴5s¹	5s+1(1)1	25.146356
44	4f¹¹5s²5p²	4f-5(5)5.4f+6(8)9	25.192432
45	4f¹²5s²5p¹	4f-5(5)5.4f+7(7)8.5p+1(3)11	25.518823
46	4f¹²5s²5p¹	4f-5(5)5.4f+7(7)6.5p+1(3)5	25.571768
47	4f¹²5s²5p¹	4f-5(5)5.4f+7(7)10.5p+1(3)11	25.685382
48	4f¹¹5s²5p²	4f-4(8)8.4f+7(7)11	25.733561
49	4f¹²5s²5p¹	4f+6(4)4.5p+1(3)3	25.861534
50	4f¹²5s²5p¹	4f-5(5)5.4f+7(7)8.5p+1(3)7	25.914135
51	4f¹²5s²5p¹	4f-5(5)5.4f+7(7)6.5p+1(3)7	26.087574
52	4f¹²5s²5p¹	4f-5(5)5.4f+7(7)8.5p+1(3)9	26.100478
53	4f¹¹5s²5p²	4f-5(5)5.4f+6(8)7	26.203062
54	4f¹¹5s²5p²	4f+5(5)5	26.274573
55	4f¹²5s²5p¹	4f+6(4)4.5p+1(3)5	26.376467
56	4f¹¹5s²5p²	4f-5(5)5.4f+6(8)3	26.602434
57	4f¹²5s²5p¹	4f-5(5)5.4f+7(7)4.5p+1(3)1	26.748723
58	4f¹²5s²5p¹	4f-5(5)5.4f+7(7)6.5p+1(3)9	26.773530
59	4f¹²5s²5p¹	4f+6(4)4.5p+1(3)7	26.925455
60	4f¹²5s²5p¹	4f-5(5)5.4f+7(7)6.5p+1(3)3	27.023513
61	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)15	27.192388
62	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)9	27.238668
63	4f¹²5s²5p¹	4f-5(5)5.4f+7(7)8.5p+1(3)5	27.250690
64	4f¹¹5s²5p²	4f+5(7)7	27.363071
65	4f¹²5s²5p¹	4f-4(8)8.5p+1(3)11	27.516542
66	4f¹²5s²5p¹	4f-4(8)8.5p+1(3)7	27.543276
67	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)11	27.655306
68	4f¹²5s²5p¹	4f-4(8)8.5p+1(3)9	27.786327
69	4f¹³5s¹5p¹	4f+7(7)7.5s+1(1)8.5p-1(1)7	28.056993
70	4f¹¹5s²5p²	4f-4(8)8.4f+7(7)9	28.081706
71	4f¹²5s²5p¹	4f-5(5)5.4f+7(7)4.5p+1(3)5	28.492190
72	4f¹¹5s²5p²	4f-5(5)5.4f+6(8)13	28.766415
73	4f¹¹5s²5p²	4f-5(5)5.4f+6(4)1	28.772590
74	4f¹²5s²5p¹	4f-5(5)5.4f+7(7)12.5p+1(3)15	28.841463
75	4f¹¹5s²5p²	4f+5(5)5	28.862296
76	4f¹¹5s²5p²	4f-4(4)4.4f+7(7)3	28.863668
77	4f¹¹5s²5p²	4f-5(5)5.4f+6(4)5	29.139885
78	4f¹²5s²5p¹	4f-4(4)4.5p+1(3)3	29.272728
79	4f¹²5s²5p¹	4f-5(5)5.4f+7(7)12.5p+1(3)9	29.390448
80	4f¹²5s²5p¹	4f+6(4)4.5p+1(3)7	29.431457
81	4f¹²5s²5p¹	4f+6(4)4.5p+1(3)1	29.536806
82	4f¹¹5s²5p²	4f-4(8)8.4f+7(7)7	29.698561
83	4f¹¹5s²5p²	4f-4(8)8.4f+7(7)7	29.938896
84	4f¹¹5s²5p²	4f-5(5)5.4f+6(8)11	29.992013
85	4f¹³5s¹5p¹	4f+7(7)7.5s+1(1)6.5p-1(1)7	30.077928
86	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)17	30.107356
87	4f¹¹5s²5p²	4f-4(8)8.4f+7(7)5	30.194314
88	4f¹²5s²5p¹	4f+6(0)0.5p+1(3)3	30.244202
89	4f¹³5s¹5p¹	4f-5(5)5.5s+1(1)4.5p-1(1)5	30.244635
90	4f¹²5s²5p¹	4f-4(4)4.5p+1(3)5	30.530323
91	4f¹³5s¹5p¹	4f+7(7)7.5s+1(1)8.5p-1(1)9	30.537856
92	4f¹¹5s²5p²	4f-3(9)9	30.925077
93	4f¹¹5s²5p²	4f-5(5)5.4f+6(4)3	31.052591
94	4f¹³5s¹5p¹	4f+7(7)7.5s+1(1)6.5p-1(1)5	31.221911
95	4f¹¹5s²5p²	4f-4(8)8.4f+7(7)13	31.222353
96	4f¹²5s²5p¹	4f-5(5)5.4f+7(7)12.5p+1(3)11	31.228435
97	4f¹²5s²5p¹	4f-5(5)5.4f+7(7)2.5p+1(3)1	31.443892
98	4f¹²5s²5p¹	4f-5(5)5.4f+7(7)2.5p+1(3)5	31.618803
99	4f¹²5s²5p¹	4f-5(5)5.4f+7(7)12.5p+1(3)13	31.626541
100	4f¹²5s²5p¹	4f+6(0)0.5p+1(3)3	31.690676
101	4f¹²5s²5p¹	4f-4(4)4.5p+1(3)7	31.855806
102	4f¹¹5s²5p²	4f-4(4)4.4f+7(7)3	31.860288
103	4f¹¹5s²5p²	4f-5(5)5.4f+6(4)9	31.868845
104	4f¹¹5s²5p²	4f-4(8)8.4f+7(7)15	32.320684
105	4f¹²5s²5p¹	4f-5(5)5.4f+7(7)2.5p+1(3)3	32.411987
106	4f¹¹5s²5p²	4f-4(8)8.4f+7(7)1	32.619662
107	4f¹¹5s²5p²	4f-4(4)4.4f+7(7)5	32.672403
108	4f¹³5s¹5p¹	4f-5(5)5.5s+1(1)6.5p-1(1)5	33.071560
109	4f¹¹5s²5p²	4f-4(4)4.4f+7(7)11	33.185265
110	4f¹³5s¹5p¹	4f-5(5)5.5s+1(1)6.5p-1(1)7	33.221250
111	4f¹²5s²5p¹	4f-4(4)4.5p+1(3)1	33.350995
112	4f¹¹5s²5p²	4f-4(4)4.4f+7(7)7	33.371350
113	4f¹¹5s²5p²	4f+5(15)15.5p-1(1)14.5p+1(3)17	33.384989
114	4f¹³5s¹5p¹	4f-5(5)5.5s+1(1)4.5p-1(1)3	33.529177
115	4f¹¹5s²5p²	4f+5(15)15.5p-1(1)14.5p+1(3)15	34.395525
116	4f¹¹5s²5p²	4f+5(15)15.5p-1(1)14.5p+1(3)13	34.979542
117	4f¹¹5s²5p²	4f-3(3)3	34.983491
118	4f¹¹5s²5p²	4f-5(5)5.4f+6(4)7	35.157994
119	4f¹¹5s²5p²	4f+5(15)15.5p-1(1)16.5p+1(3)19	35.632188
120	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)13.5p-1(1)14.5p+1(3)11	35.873969
121	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)13.5p-1(1)12.5p+1(3)15	36.103905
122	4f¹¹5s²5p²	4f-3(5)5	36.132441
123	4f¹¹5s²5p²	4f+5(15)15.5p-1(1)16.5p+1(3)17	36.289379
124	4f¹¹5s²5p²	4f+5(11)11.5p-1(1)10.5p+1(3)13	36.421597
125	4f¹¹5s²5p²	4f+5(9)9.5p-1(1)8.5p+1(3)11	36.524088
126	4f¹¹5s²5p²	4f+5(9)9.5p-1(1)8.5p+1(3)9	36.532534
127	4f¹¹5s²5p²	4f+5(15)15.5p-1(1)16.5p+1(3)15	36.572398
128	4f¹¹5s²5p²	4f+5(9)9.5p-1(1)8.5p+1(3)9	36.677277
129	4f¹¹5s²5p²	4f+5(15)15.5p-1(1)16.5p+1(3)13	36.697402
130	4f¹¹5s²5p²	4f-4(4)4.4f+7(7)9	36.795762
131	4f¹¹5s²5p²	4f+5(9)9.5p-1(1)10.5p+1(3)7	36.952634
132	4f¹¹5s²5p²	4f+5(15)15.5p-1(1)14.5p+1(3)11	37.082975
133	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)13.5p-1(1)14.5p+1(3)13	37.411724
134	4f¹¹5s²5p²	4f+5(9)9.5p-1(1)10.5p+1(3)11	37.597102
135	4f¹¹5s²5p²	4f+5(9)9.5p-1(1)8.5p+1(3)7	37.813602
136	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)13.5p-1(1)14.5p+1(3)17	37.826275
137	4f¹¹5s²5p²	4f+5(3)3.5p-1(1)2.5p+1(3)5	37.898919
138	4f¹²5s¹5p²	4f+6(12)12.5s+1(1)13	38.071969
139	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)13.5p-1(1)12.5p+1(3)11	38.248034
140	4f¹¹5s²5p²	4f+5(3)3.5p-1(1)4.5p+1(3)3	38.277848
141	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)9.5p-1(1)8.5p+1(3)9	38.297614
142	4f¹¹5s²5p²	4f-5(5)5.4f+6(8)9.5p-1(1)8.5p+1(3)11	38.321917
143	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)13.5p-1(1)14.5p+1(3)13	38.367848
144	4f¹¹5s²5p²	4f-5(5)5.4f+6(8)5.5p-1(1)4.5p+1(3)5	38.377390
145	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)13.5p-1(1)14.5p+1(3)15	38.419868
146	4f¹¹5s²5p²	4f+5(11)11.5p-1(1)10.5p+1(3)9	38.462512
147	4f¹¹5s²5p²	4f+5(9)9.5p-1(1)10.5p+1(3)13	38.561854
148	4f¹¹5s²5p²	4f+5(3)3.5p-1(1)4.5p+1(3)1	38.700658
149	4f¹¹5s²5p²	4f+5(9)9.5p-1(1)10.5p+1(3)7	38.714756
150	4f¹¹5s²5p²	4f+5(11)11.5p-1(1)10.5p+1(3)9	38.717201
151	4f¹¹5s²5p²	4f+5(9)9.5p-1(1)8.5p+1(3)7	38.777407
152	4f¹¹5s²5p²	4f+5(9)9.5p-1(1)8.5p+1(3)5	38.786312
153	4f¹¹5s²5p²	4f+5(11)11.5p-1(1)12.5p+1(3)15	38.840427
154	4f¹²5s²5p¹	4f-4(0)0.5p+1(3)3	38.850279
155	4f¹¹5s²5p²	4f+5(9)9.5p-1(1)10.5p+1(3)11	38.857099
156	4f¹¹5s²5p²	4f+5(11)11.5p-1(1)10.5p+1(3)13	38.931170
157	4f¹¹5s²5p²	4f-4(8)8.4f+7(7)11.5p-1(1)12.5p+1(3)11	39.036573
158	4f¹²5s¹5p²	4f+6(12)12.5s+1(1)11	39.094106
159	4f¹¹5s²5p²	4f+5(11)11.5p-1(1)12.5p+1(3)9	39.211350
160	4f¹²5s¹5p²	4f+6(8)8.5s+1(1)9	39.332591
161	4f¹¹5s²5p²	4f+5(11)11.5p-1(1)12.5p+1(3)13	39.344217
162	4f¹¹5s²5p²	4f+5(9)9.5p-1(1)10.5p+1(3)9	39.354890
163	4f¹¹5s²5p²	4f-5(5)5.4f+6(8)3.5p-1(1)4.5p+1(3)3	39.466359
164	4f¹¹5s²5p²	4f+5(5)5.5p-1(1)4.5p+1(3)7	39.469231
165	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)13.5p-1(1)12.5p+1(3)9	39.696083
166	4f¹¹5s²5p²	4f+5(3)3.5p-1(1)4.5p+1(3)5	39.739705
167	4f¹¹5s²5p²	4f+5(3)3.5p-1(1)4.5p+1(3)7	39.748882
168	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)9.5p-1(1)8.5p+1(3)11	39.768124
169	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)15.5p-1(1)14.5p+1(3)17	39.864491
170	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)13.5p-1(1)12.5p+1(3)11	39.955178
171	4f¹¹5s²5p²	4f-5(5)5.4f+6(4)3.5p-1(1)4.5p+1(3)1	40.023281
172	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)15.5p-1(1)16.5p+1(3)13	40.030831
173	4f¹¹5s²5p²	4f+5(3)3.5p-1(1)4.5p+1(3)5	40.042976
174	4f¹²5s¹5p²	4f+6(8)8.5s+1(1)7	40.076237
175	4f¹¹5s²5p²	4f-5(5)5.4f+6(8)3.5p-1(1)4.5p+1(3)7	40.103966
176	4f¹¹5s²5p²	4f-5(5)5.4f+6(8)9.5p-1(1)10.5p+1(3)13	40.159488
177	4f¹¹5s²5p²	4f+5(3)3.5p-1(1)4.5p+1(3)5	40.186407
178	4f¹¹5s²5p²	4f+5(3)3.5p-1(1)2.5p+1(3)3	40.201850
179	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)13.5p-1(1)12.5p+1(3)9	40.205703
180	4f¹¹5s²5p²	4f+5(5)5.5p-1(1)6.5p+1(3)3	40.289325
181	4f¹¹5s²5p²	4f-5(5)5.4f+6(8)9.5p-1(1)8.5p+1(3)11	40.382701
182	4f¹¹5s²5p²	4f-5(5)5.4f+6(0)5	40.407623
183	4f¹¹5s²5p²	4f-4(8)8.4f+7(7)11.5p-1(1)12.5p+1(3)15	40.546845
184	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)9.5p-1(1)8.5p+1(3)7	40.567874
185	4f¹¹5s²5p²	4f-4(8)8.4f+7(7)11.5p-1(1)12.5p+1(3)9	40.574136
186	4f¹¹5s²5p²	4f-5(5)5.4f+6(8)13.5p-1(1)14.5p+1(3)11	40.623030
187	4f¹¹5s²5p²	4f-5(5)5.4f+6(8)9.5p-1(1)8.5p+1(3)7	40.652418
188	4f¹¹5s²5p²	4f-5(5)5.4f+6(8)3.5p-1(1)2.5p+1(3)3	40.706965
189	4f¹¹5s²5p²	4f-5(5)5.4f+6(8)9.5p-1(1)8.5p+1(3)9	40.755795
190	4f¹¹5s²5p²	4f-5(5)5.4f+6(4)1.5p-1(1)2.5p+1(3)1	40.779964
191	4f¹¹5s²5p²	4f+5(11)11.5p-1(1)10.5p+1(3)7	40.854550
192	4f¹²5s¹5p²	4f-5(5)5.4f+7(7)10.5s+1(1)9	40.863392
193	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)15.5p-1(1)16.5p+1(3)13	40.890074
194	4f¹¹5s²5p²	4f-5(5)5.4f+6(8)7.5p-1(1)8.5p+1(3)11	40.891647
195	4f¹¹5s²5p²	4f+5(9)9.5p-1(1)8.5p+1(3)5	40.977267
196	4f¹¹5s²5p²	4f-5(5)5.4f+6(8)7.5p-1(1)8.5p+1(3)9	41.011051
197	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)11.5p-1(1)12.5p+1(3)13	41.066343
198	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)15.5p-1(1)16.5p+1(3)15	41.092734
199	4f¹¹5s²5p²	4f-5(5)5.4f+6(4)1.5p-1(1)2.5p+1(3)3	41.127133
200	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)9.5p-1(1)10.5p+1(3)7	41.160989
201	4f¹¹5s²5p²	4f-5(5)5.4f+6(4)1.5p-1(1)2.5p+1(3)1	41.192857
202	4f¹¹5s²5p²	4f-5(5)5.4f+6(8)7.5p-1(1)6.5p+1(3)9	41.210887
203	4f¹¹5s²5p²	4f-5(5)5.4f+6(8)7.5p-1(1)8.5p+1(3)5	41.254861
204	4f¹¹5s²5p²	4f-5(5)5.4f+6(8)5.5p-1(1)4.5p+1(3)5	41.317661
205	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)15.5p-1(1)16.5p+1(3)19	41.471568
206	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)9.5p-1(1)8.5p+1(3)11	41.504783
207	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)11.5p-1(1)12.5p+1(3)11	41.534879
208	4f¹²5s¹5p²	4f+6(4)4.5s+1(1)3	41.558156
209	4f¹¹5s²5p²	4f+5(5)5.5p-1(1)6.5p+1(3)9	41.567579
210	4f¹²5s¹5p²	4f-5(5)5.4f+7(7)6.5s+1(1)5	41.581960
211	4f¹¹5s²5p²	4f+5(11)11.5p-1(1)10.5p+1(3)7	41.590698
212	4f¹¹5s²5p²	4f-5(5)5.4f+6(8)3.5p-1(1)4.5p+1(3)5	41.615627
213	4f¹¹5s²5p²	4f-4(8)8.4f+7(7)3.5p-1(1)4.5p+1(3)5	41.684795
214	4f¹¹5s²5p²	4f-5(5)5.4f+6(8)3.5p-1(1)2.5p+1(3)1	41.689852
215	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)9.5p-1(1)10.5p+1(3)9	41.695204
216	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)9.5p-1(1)8.5p+1(3)7	41.718644
217	4f¹²5s¹5p²	4f-5(5)5.4f+7(7)8.5s+1(1)7	41.720355
218	4f¹¹5s²5p²	4f-4(8)8.4f+7(7)9.5p-1(1)10.5p+1(3)11	41.740916
219	4f¹¹5s²5p²	4f-5(5)5.4f+6(8)3.5p-1(1)4.5p+1(3)3	41.772383
220	4f¹¹5s²5p²	4f+5(5)5.5p-1(1)4.5p+1(3)1	41.821878
221	4f¹¹5s²5p²	4f-5(5)5.4f+6(8)13.5p-1(1)12.5p+1(3)15	41.824746
222	4f¹³5s¹5p¹	4f+7(7)7.5s+1(1)8.5p+1(3)11	41.889066
223	4f¹¹5s²5p²	4f-5(5)5.4f+6(8)9.5p-1(1)10.5p+1(3)9	41.903860
224	4f¹¹5s²5p²	4f-5(5)5.4f+6(8)7.5p-1(1)8.5p+1(3)7	41.906544
225	4f¹²5s¹5p²	4f-5(5)5.4f+7(7)10.5s+1(1)11	41.954094
226	4f¹¹5s²5p²	4f+5(7)7.5p-1(1)8.5p+1(3)7	42.030961
227	4f¹¹5s²5p²	4f+5(5)5.5p-1(1)4.5p+1(3)3	42.044655
228	4f¹¹5s²5p²	4f+5(5)5.5p-1(1)6.5p+1(3)5	42.063989
229	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)15.5p-1(1)14.5p+1(3)11	42.163110
230	4f¹¹5s²5p²	4f-4(0)0.4f+7(7)7	42.205120
231	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)15.5p-1(1)14.5p+1(3)13	42.221158
232	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)11.5p-1(1)12.5p+1(3)15	42.276307
233	4f¹¹5s²5p²	4f-5(5)5.4f+6(8)3.5p-1(1)4.5p+1(3)7	42.291003
234	4f¹¹5s²5p²	4f-5(5)5.4f+6(8)5.5p-1(1)6.5p+1(3)9	42.294626
235	4f¹¹5s²5p²	4f-5(5)5.4f+6(8)7.5p-1(1)6.5p+1(3)5	42.367551
236	4f¹¹5s²5p²	4f-5(5)5.4f+6(8)7.5p-1(1)6.5p+1(3)3	42.411801
237	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)9.5p-1(1)10.5p+1(3)13	42.426365
238	4f¹¹5s²5p²	4f-4(0)0.4f+7(7)7	42.471082
239	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)17.5p-1(1)16.5p+1(3)19	42.488306
240	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)17.5p-1(1)18.5p+1(3)15	42.490099
241	4f¹¹5s²5p²	4f-4(8)8.4f+7(7)9.5p-1(1)10.5p+1(3)13	42.510407
242	4f¹¹5s²5p²	4f-5(5)5.4f+6(8)3.5p-1(1)4.5p+1(3)3	42.601749
243	4f¹¹5s²5p²	4f+5(7)7.5p-1(1)8.5p+1(3)11	42.668342
244	4f¹²5s¹5p²	4f-5(5)5.4f+7(7)8.5s+1(1)9	42.675456
245	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)11.5p-1(1)12.5p+1(3)9	42.676572
246	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)15.5p-1(1)16.5p+1(3)17	42.747113
247	4f¹¹5s²5p²	4f-4(4)4.4f+7(7)3.5p-1(1)2.5p+1(3)5	42.761996
248	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)9.5p-1(1)10.5p+1(3)7	42.778821
249	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)11.5p-1(1)12.5p+1(3)11	42.844266
250	4f¹³5s¹5p¹	4f+7(7)7.5s+1(1)6.5p+1(3)3	42.846710
251	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)9.5p-1(1)8.5p+1(3)9	42.850480
252	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)15.5p-1(1)16.5p+1(3)13	42.883478
253	4f¹¹5s²5p²	4f-4(4)4.4f+7(7)3.5p-1(1)4.5p+1(3)1	42.940906
254	4f¹¹5s²5p²	4f-5(5)5.4f+6(4)5.5p-1(1)6.5p+1(3)5	42.960119
255	4f¹¹5s²5p²	4f+5(7)7.5p-1(1)8.5p+1(3)11	42.979710
256	4f¹¹5s²5p²	4f-5(5)5.4f+6(8)13.5p-1(1)14.5p+1(3)17	43.036815
257	4f¹¹5s²5p²	4f-3(9)9.5p-1(1)10.5p+1(3)9	43.045039
258	4f¹²5s¹5p²	4f-5(5)5.4f+7(7)6.5s+1(1)7	43.067672
259	4f¹¹5s²5p²	4f-5(5)5.4f+6(4)5.5p-1(1)6.5p+1(3)7	43.115484
260	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)9.5p-1(1)8.5p+1(3)5	43.123252
261	4f¹¹5s²5p²	4f-4(8)8.4f+7(7)1.5p-1(1)2.5p+1(3)1	43.184025
262	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)9.5p-1(1)10.5p+1(3)13	43.193490
263	4f¹³5s¹5p¹	4f+7(7)7.5s+1(1)6.5p+1(3)5	43.206794
264	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)9.5p-1(1)8.5p+1(3)7	43.247479
265	4f¹¹5s²5p²	4f-5(5)5.4f+6(4)1.5p-1(1)0.5p+1(3)3	43.253889
266	4f¹³5s¹5p¹	4f-5(5)5.5s+1(1)4.5p+1(3)1	43.258331
267	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)15.5p-1(1)14.5p+1(3)11	43.283855
268	4f¹²5s¹5p²	4f+6(4)4.5s+1(1)5	43.285472
269	4f¹¹5s²5p²	4f+5(7)7.5p-1(1)6.5p+1(3)3	43.317624
270	4f¹¹5s²5p²	4f-5(5)5.4f+6(4)7.5p-1(1)8.5p+1(3)9	43.319875
271	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)17.5p-1(1)18.5p+1(3)15	43.352594
272	4f¹¹5s²5p²	4f-4(8)8.4f+7(7)9.5p-1(1)8.5p+1(3)5	43.417388
273	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)11.5p-1(1)10.5p+1(3)9	43.498409
274	4f¹¹5s²5p²	4f-4(8)8.4f+7(7)5.5p-1(1)6.5p+1(3)7	43.511747
275	4f¹¹5s²5p²	4f-3(9)9.5p-1(1)8.5p+1(3)7	43.580865
276	4f¹¹5s²5p²	4f-4(8)8.4f+7(7)7.5p-1(1)8.5p+1(3)5	43.641796
277	4f¹³5s¹5p¹	4f+7(7)7.5s+1(1)6.5p+1(3)7	43.649705
278	4f¹¹5s²5p²	4f-4(4)4.4f+7(7)5.5p-1(1)6.5p+1(3)3	43.660656
279	4f¹³5s¹5p¹	4f+7(7)7.5s+1(1)8.5p+1(3)9	43.671016
280	4f¹¹5s²5p²	4f-4(8)8.4f+7(7)15.5p-1(1)16.5p+1(3)13	43.717882
281	4f¹¹5s²5p²	4f-4(8)8.4f+7(7)9.5p-1(1)10.5p+1(3)9	43.750006
282	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)9.5p-1(1)10.5p+1(3)11	43.751161
283	4f¹¹5s²5p²	4f-4(8)8.4f+7(7)7.5p-1(1)8.5p+1(3)7	43.810325
284	4f¹¹5s²5p²	4f-5(5)5.4f+6(8)13.5p-1(1)12.5p+1(3)13	43.816105
285	4f¹¹5s²5p²	4f-5(5)5.4f+6(4)1.5p-1(1)2.5p+1(3)5	43.827070
286	4f¹¹5s²5p²	4f-4(8)8.4f+7(7)7.5p-1(1)6.5p+1(3)9	43.851458
287	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)11.5p-1(1)10.5p+1(3)7	43.912980
288	4f¹¹5s²5p²	4f-4(8)8.4f+7(7)3.5p-1(1)4.5p+1(3)5	43.980542
289	4f¹¹5s²5p²	4f-3(9)9.5p-1(1)10.5p+1(3)11	44.031655
290	4f¹¹5s²5p²	4f-5(5)5.4f+6(8)5.5p-1(1)6.5p+1(3)3	44.052047
291	4f¹¹5s²5p²	4f-5(5)5.4f+6(8)13.5p-1(1)14.5p+1(3)15	44.055037
292	4f¹¹5s²5p²	4f-5(5)5.4f+6(4)5.5p-1(1)6.5p+1(3)9	44.067255
293	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)17.5p-1(1)18.5p+1(3)21	44.093153
294	4f¹¹5s²5p²	4f-4(4)4.4f+7(7)5.5p-1(1)4.5p+1(3)7	44.180961
295	4f¹¹5s²5p²	4f-4(8)8.4f+7(7)13.5p-1(1)12.5p+1(3)15	44.272026
296	4f¹¹5s²5p²	4f-4(4)4.4f+7(7)3.5p-1(1)2.5p+1(3)3	44.273736
297	4f¹¹5s²5p²	4f-4(8)8.4f+7(7)15.5p-1(1)16.5p+1(3)13	44.307366
298	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)17.5p-1(1)18.5p+1(3)17	44.323538
299	4f¹¹5s²5p²	4f-5(5)5.4f+6(4)1.5p-1(1)2.5p+1(3)5	44.328986
300	4f¹¹5s²5p²	4f-5(5)5.4f+6(4)3.5p-1(1)4.5p+1(3)7	44.359708
301	4f¹¹5s²5p²	4f-5(5)5.4f+6(8)13.5p-1(1)12.5p+1(3)11	44.376938
302	4f¹¹5s²5p²	4f-4(8)8.4f+7(7)13.5p-1(1)12.5p+1(3)9	44.401158
303	4f¹¹5s²5p²	4f-4(4)4.4f+7(7)3.5p-1(1)4.5p+1(3)1	44.423800
304	4f¹¹5s²5p²	4f-4(4)4.4f+7(7)5.5p-1(1)6.5p+1(3)5	44.470206
305	4f¹¹5s²5p²	4f+5(5)5.5p-1(1)6.5p+1(3)3	44.493374
306	4f¹¹5s²5p²	4f-5(5)5.4f+6(8)11.5p-1(1)10.5p+1(3)11	44.531032
307	4f¹¹5s²5p²	4f-4(4)4.4f+7(7)3.5p-1(1)2.5p+1(3)1	44.542990
308	4f¹¹5s²5p²	4f+5(5)5.5p-1(1)4.5p+1(3)5	44.577555
309	4f¹¹5s²5p²	4f+5(5)5.5p-1(1)6.5p+1(3)7	44.585082
310	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)17.5p-1(1)16.5p+1(3)13	44.619176
311	4f¹²5s¹5p²	4f-4(8)8.5s+1(1)7	44.655880
312	4f¹¹5s²5p²	4f-5(5)5.4f+6(4)5.5p-1(1)6.5p+1(3)9	44.663143
313	4f¹¹5s²5p²	4f-4(4)4.4f+7(7)3.5p-1(1)2.5p+1(3)5	44.734290
314	4f¹¹5s²5p²	4f-5(5)5.4f+6(4)5.5p-1(1)4.5p+1(3)7	44.812548
315	4f¹¹5s²5p²	4f-4(8)8.4f+7(7)7.5p-1(1)8.5p+1(3)11	44.879029
316	4f¹¹5s²5p²	4f-5(5)5.4f+6(4)5.5p-1(1)4.5p+1(3)3	44.933982
317	4f¹³5s¹5p¹	4f-5(5)5.5s+1(1)4.5p+1(3)3	45.024375
318	4f¹¹5s²5p²	4f-5(5)5.4f+6(4)5.5p-1(1)4.5p+1(3)5	45.026303
319	4f¹²5s¹5p²	4f-5(5)5.4f+7(7)4.5s+1(1)5	45.079574
320	4f¹¹5s²5p²	4f+5(5)5.5p-1(1)4.5p+1(3)1	45.082661
321	4f¹¹5s²5p²	4f-5(5)5.4f+6(8)11.5p-1(1)12.5p+1(3)15	45.085685
322	4f¹²5s¹5p²	4f+6(4)4.5s+1(1)3	45.096066
323	4f¹¹5s²5p²	4f-5(5)5.4f+6(8)11.5p-1(1)10.5p+1(3)9	45.139443
324	4f¹¹5s²5p²	4f-5(5)5.4f+6(8)5.5p-1(1)4.5p+1(3)3	45.160972
325	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)7.5p-1(1)6.5p+1(3)7	45.169732
326	4f¹³5s¹5p¹	4f-5(5)5.5s+1(1)6.5p+1(3)9	45.171113
327	4f¹¹5s²5p²	4f-4(8)8.4f+7(7)15.5p-1(1)14.5p+1(3)17	45.207091
328	4f¹²5s¹5p²	4f+6(0)0.5s+1(1)1	45.226338
329	4f¹²5s¹5p²	4f-4(8)8.5s+1(1)9	45.263813
330	4f¹¹5s²5p²	4f-5(5)5.4f+6(8)5.5p-1(1)6.5p+1(3)9	45.287098
331	4f¹¹5s²5p²	4f-5(5)5.4f+6(8)11.5p-1(1)10.5p+1(3)7	45.311729
332	4f¹¹5s²5p²	4f-3(9)9.5p-1(1)10.5p+1(3)13	45.364459
333	4f¹¹5s²5p²	4f-4(8)8.4f+7(7)7.5p-1(1)8.5p+1(3)11	45.366640
334	4f¹¹5s²5p²	4f-4(8)8.4f+7(7)5.5p-1(1)4.5p+1(3)7	45.369971
335	4f¹¹5s²5p²	4f-5(5)5.4f+6(4)3.5p-1(1)4.5p+1(3)5	45.394036
336	4f¹¹5s²5p²	4f-4(8)8.4f+7(7)7.5p-1(1)6.5p+1(3)5	45.452376
337	4f¹¹5s²5p²	4f-5(5)5.4f+6(8)11.5p-1(1)12.5p+1(3)13	45.454850
338	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)7.5p-1(1)8.5p+1(3)11	45.503849
339	4f¹¹5s²5p²	4f-4(8)8.4f+7(7)5.5p-1(1)6.5p+1(3)9	45.532680
340	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)7.5p-1(1)6.5p+1(3)3	45.547802
341	4f¹¹5s²5p²	4f-3(9)9.5p-1(1)8.5p+1(3)9	45.569721
342	4f¹¹5s²5p²	4f-4(8)8.4f+7(7)5.5p-1(1)4.5p+1(3)3	45.714391
343	4f¹¹5s²5p²	4f-5(5)5.4f+6(8)11.5p-1(1)10.5p+1(3)11	45.747075
344	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)7.5p-1(1)6.5p+1(3)5	45.758919
345	4f¹¹5s²5p²	4f-4(4)4.4f+7(7)3.5p-1(1)4.5p+1(3)1	45.785356
346	4f¹¹5s²5p²	4f-3(9)9.5p-1(1)8.5p+1(3)7	45.798358
347	4f¹¹5s²5p²	4f-3(9)9.5p-1(1)8.5p+1(3)9	45.878309
348	4f¹¹5s²5p²	4f-3(3)3.5p-1(1)4.5p+1(3)1	45.896710
349	4f¹¹5s²5p²	4f-4(8)8.4f+7(7)3.5p-1(1)2.5p+1(3)3	45.906397
350	4f¹¹5s²5p²	4f-4(8)8.4f+7(7)3.5p-1(1)4.5p+1(3)7	45.926221
351	4f¹³5s¹5p¹	4f-5(5)5.5s+1(1)4.5p+1(3)5	45.997353
352	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)17.5p-1(1)16.5p+1(3)13	46.001588
353	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)7.5p-1(1)6.5p+1(3)5	46.007526
354	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)17.5p-1(1)16.5p+1(3)17	46.084963
355	4f¹¹5s²5p²	4f-3(9)9.5p-1(1)8.5p+1(3)11	46.106557
356	4f¹¹5s²5p²	4f-4(8)8.4f+7(7)15.5p-1(1)16.5p+1(3)19	46.119690
357	4f¹³5s¹5p¹	4f-5(5)5.5s+1(1)6.5p+1(3)7	46.145634
358	4f¹¹5s²5p²	4f-4(8)8.4f+7(7)7.5p-1(1)6.5p+1(3)3	46.160789
359	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)17.5p-1(1)18.5p+1(3)19	46.198266
360	4f¹¹5s²5p²	4f-3(9)9.5p-1(1)8.5p+1(3)7	46.238815
361	4f¹¹5s²5p²	4f-5(5)5.4f+6(4)3.5p-1(1)2.5p+1(3)3	46.264864
362	4f¹²5s¹5p²	4f-5(5)5.4f+7(7)2.5s+1(1)3	46.305166
363	4f¹²5s¹5p²	4f-5(5)5.4f+7(7)12.5s+1(1)13	46.313076
364	4f¹¹5s²5p²	4f-4(4)4.4f+7(7)11.5p-1(1)10.5p+1(3)13	46.330883
365	4f¹¹5s²5p²	4f-4(8)8.4f+7(7)5.5p-1(1)6.5p+1(3)9	46.359567
366	4f¹²5s¹5p²	4f-5(5)5.4f+7(7)12.5s+1(1)11	46.359947
367	4f¹¹5s²5p²	4f-4(8)8.4f+7(7)13.5p-1(1)14.5p+1(3)15	46.375372
368	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)17.5p-1(1)18.5p+1(3)17	46.447493
369	4f¹¹5s²5p²	4f-4(8)8.4f+7(7)5.5p-1(1)4.5p+1(3)1	46.467329
370	4f¹¹5s²5p²	4f-4(8)8.4f+7(7)13.5p-1(1)12.5p+1(3)11	46.470016
371	4f¹¹5s²5p²	4f-4(8)8.4f+7(7)15.5p-1(1)16.5p+1(3)15	46.479449
372	4f¹¹5s²5p²	4f-3(3)3.5p-1(1)4.5p+1(3)5	46.524453
373	4f¹¹5s²5p²	4f-4(8)8.4f+7(7)5.5p-1(1)4.5p+1(3)7	46.566212
374	4f¹¹5s²5p²	4f-4(8)8.4f+7(7)1.5p-1(1)2.5p+1(3)3	46.614030
375	4f¹¹5s²5p²	4f-3(3)3.5p-1(1)4.5p+1(3)5	46.627077
376	4f¹¹5s²5p²	4f-5(5)5.4f+6(4)3.5p-1(1)4.5p+1(3)7	46.762017
377	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)7.5p-1(1)8.5p+1(3)9	46.768387
378	4f¹¹5s²5p²	4f-4(4)4.4f+7(7)11.5p-1(1)12.5p+1(3)9	46.837656
379	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)17.5p-1(1)16.5p+1(3)15	46.923650
380	4f¹¹5s²5p²	4f-4(4)4.4f+7(7)5.5p-1(1)4.5p+1(3)1	46.925950
381	4f¹¹5s²5p²	4f-4(4)4.4f+7(7)3.5p-1(1)2.5p+1(3)3	46.940582
382	4f¹¹5s²5p²	4f-4(8)8.4f+7(7)15.5p-1(1)14.5p+1(3)11	46.990451
383	4f¹¹5s²5p²	4f-4(8)8.4f+7(7)13.5p-1(1)12.5p+1(3)9	47.012767
384	4f¹¹5s²5p²	4f-4(8)8.4f+7(7)3.5p-1(1)2.5p+1(3)5	47.019958
385	4f¹¹5s²5p²	4f-5(5)5.4f+6(4)9.5p-1(1)10.5p+1(3)13	47.046126
386	4f¹¹5s²5p²	4f+5(7)7.5p-1(1)8.5p+1(3)5	47.224165
387	4f¹¹5s²5p²	4f-4(8)8.4f+7(7)13.5p-1(1)12.5p+1(3)13	47.329489
388	4f¹¹5s²5p²	4f-4(8)8.4f+7(7)1.5p-1(1)2.5p+1(3)3	47.357200
389	4f¹¹5s²5p²	4f-4(8)8.4f+7(7)3.5p-1(1)4.5p+1(3)7	47.366743
390	4f¹¹5s²5p²	4f-4(8)8.4f+7(7)15.5p-1(1)14.5p+1(3)11	47.371560
391	4f¹¹5s²5p²	4f-4(8)8.4f+7(7)1.5p-1(1)2.5p+1(3)5	47.400267
392	4f¹¹5s²5p²	4f-5(5)5.4f+6(4)9.5p-1(1)8.5p+1(3)9	47.490240
393	4f¹²5s¹5p²	4f+6(12)12.5s+1(1)13.5p-1(1)12.5p+1(3)15	47.566220
394	4f¹¹5s²5p²	4f-4(4)4.4f+7(7)3.5p-1(1)2.5p+1(3)1	47.576112
395	4f¹²5s¹5p²	4f-4(4)4.5s+1(1)5	47.608356
396	4f¹¹5s²5p²	4f-5(5)5.4f+6(4)9.5p-1(1)8.5p+1(3)7	47.626404
397	4f¹¹5s²5p²	4f-4(8)8.4f+7(7)3.5p-1(1)4.5p+1(3)3	47.630702
398	4f¹¹5s²5p²	4f-4(4)4.4f+7(7)7.5p-1(1)8.5p+1(3)5	47.856467
399	4f¹¹5s²5p²	4f-5(5)5.4f+6(4)9.5p-1(1)8.5p+1(3)7	47.906232
400	4f¹¹5s²5p²	4f-4(4)4.4f+7(7)5.5p-1(1)6.5p+1(3)9	47.942764
401	4f¹¹5s²5p²	4f-4(4)4.4f+7(7)5.5p-1(1)4.5p+1(3)3	48.044767
402	4f¹¹5s²5p²	4f-4(4)4.4f+7(7)11.5p-1(1)12.5p+1(3)15	48.051851
403	4f¹¹5s²5p²	4f-4(4)4.4f+7(7)11.5p-1(1)12.5p+1(3)11	48.152857
404	4f¹¹5s²5p²	4f-4(4)4.4f+7(7)5.5p-1(1)4.5p+1(3)5	48.241588
405	4f¹¹5s²5p²	4f-4(8)8.4f+7(7)15.5p-1(1)16.5p+1(3)17	48.262896
406	4f¹¹5s²5p²	4f-4(4)4.4f+7(7)5.5p-1(1)6.5p+1(3)7	48.340247
407	4f¹¹5s²5p²	4f-4(8)8.4f+7(7)1.5p-1(1)2.5p+1(3)5	48.405696
408	4f¹²5s¹5p²	4f-5(5)5.4f+7(7)2.5s+1(1)1	48.416353
409	4f¹¹5s²5p²	4f-4(4)4.4f+7(7)11.5p-1(1)12.5p+1(3)13	48.461446
410	4f¹¹5s²5p²	4f-4(4)4.4f+7(7)7.5p-1(1)8.5p+1(3)11	48.477197
411	4f¹¹5s²5p²	4f-3(3)3.5p-1(1)2.5p+1(3)1	48.497669
412	4f¹¹5s²5p²	4f-4(4)4.4f+7(7)11.5p-1(1)10.5p+1(3)7	48.743022
413	4f¹¹5s²5p²	4f-4(8)8.4f+7(7)3.5p-1(1)2.5p+1(3)5	48.754213
414	4f¹¹5s²5p²	4f-4(4)4.4f+7(7)11.5p-1(1)10.5p+1(3)9	48.792651
415	4f¹¹5s²5p²	4f-4(4)4.4f+7(7)11.5p-1(1)10.5p+1(3)11	48.831990
416	4f¹¹5s²5p²	4f-4(8)8.4f+7(7)5.5p-1(1)4.5p+1(3)1	48.876547
417	4f¹²5s¹5p²	4f-5(5)5.4f+7(7)4.5s+1(1)3	48.891319
418	4f¹¹5s²5p²	4f-4(8)8.4f+7(7)15.5p-1(1)14.5p+1(3)13	48.923501
419	4f¹¹5s²5p²	4f-4(4)4.4f+7(7)7.5p-1(1)6.5p+1(3)5	48.991206
420	4f¹¹5s²5p²	4f-4(8)8.4f+7(7)15.5p-1(1)14.5p+1(3)15	49.005761
421	4f¹¹5s²5p²	4f-4(4)4.4f+7(7)7.5p-1(1)8.5p+1(3)9	49.073201
422	4f¹¹5s²5p²	4f-4(8)8.4f+7(7)1.5p-1(1)0.5p+1(3)3	49.092208
423	4f¹¹5s²5p²	4f-5(5)5.4f+6(4)7.5p-1(1)8.5p+1(3)7	49.107584
424	4f¹²5s¹5p²	4f+6(8)8.5s+1(1)9.5p-1(1)8.5p+1(3)11	49.225409
425	4f¹¹5s²5p²	4f-4(4)4.4f+7(7)7.5p-1(1)6.5p+1(3)3	49.318118
426	4f¹¹5s²5p²	4f-4(4)4.4f+7(7)5.5p-1(1)4.5p+1(3)5	49.398585
427	4f¹¹5s²5p²	4f-3(3)3.5p-1(1)4.5p+1(3)7	49.458758
428	4f¹²5s¹5p²	4f+6(12)12.5s+1(1)13.5p-1(1)12.5p+1(3)13	49.511467
429	4f¹²5s¹5p²	4f+6(8)8.5s+1(1)9.5p-1(1)8.5p+1(3)9	49.549600
430	4f¹¹5s²5p²	4f-5(5)5.4f+6(4)7.5p-1(1)6.5p+1(3)9	49.803106
431	4f¹¹5s²5p²	4f-3(3)3.5p-1(1)4.5p+1(3)3	49.819068
432	4f¹¹5s²5p²	4f-4(4)4.4f+7(7)5.5p-1(1)6.5p+1(3)7	49.856027
433	4f¹³5s¹5p¹	4f+7(7)7.5s+1(1)8.5p+1(3)5	49.881682
434	4f¹³5s¹5p¹	4f+7(7)7.5s+1(1)6.5p+1(3)9	49.987168
435	4f¹¹5s²5p²	4f-3(3)3.5p-1(1)2.5p+1(3)3	50.028605
436	4f¹¹5s²5p²	4f-5(5)5.4f+6(4)7.5p-1(1)8.5p+1(3)5	50.077842
437	4f¹¹5s²5p²	4f-4(4)4.4f+7(7)9.5p-1(1)10.5p+1(3)7	50.111402
438	4f¹²5s¹5p²	4f-5(5)5.4f+7(7)10.5s+1(1)9.5p-1(1)10.5p+1(3)7	50.183762
439	4f¹²5s¹5p²	4f+6(8)8.5s+1(1)9.5p-1(1)8.5p+1(3)9	50.198350
440	4f¹¹5s²5p²	4f+5(15)15.5p+2(4)19	50.226742
441	4f¹²5s¹5p²	4f-5(5)5.4f+7(7)8.5s+1(1)7.5p-1(1)8.5p+1(3)5	50.328400
442	4f¹²5s¹5p²	4f+6(8)8.5s+1(1)7.5p-1(1)8.5p+1(3)7	50.426385
443	4f¹¹5s²5p²	4f-3(3)3.5p-1(1)2.5p+1(3)1	50.466901
444	4f¹¹5s²5p²	4f-4(4)4.4f+7(7)9.5p-1(1)10.5p+1(3)7	50.502712
445	4f¹²5s¹5p²	4f+6(8)8.5s+1(1)9.5p-1(1)8.5p+1(3)11	50.590776
446	4f¹¹5s²5p²	4f-5(5)5.4f+6(4)7.5p-1(1)6.5p+1(3)9	50.597918
447	4f¹¹5s²5p²	4f-5(5)5.4f+6(4)7.5p-1(1)8.5p+1(3)11	50.610624
448	4f¹¹5s²5p²	4f-4(4)4.4f+7(7)9.5p-1(1)8.5p+1(3)5	50.949017
449	4f¹¹5s²5p²	4f-3(5)5.5p-1(1)6.5p+1(3)9	51.020195
450	4f¹¹5s²5p²	4f-4(4)4.4f+7(7)9.5p-1(1)8.5p+1(3)11	51.068131
451	4f¹³5s¹5p¹	4f+7(7)7.5s+1(1)8.5p+1(3)7	51.070448
452	4f¹¹5s²5p²	4f+5(15)15.5p+2(4)17	51.116024
453	4f¹²5s¹5p²	4f-5(5)5.4f+7(7)10.5s+1(1)11.5p-1(1)10.5p+1(3)13	51.334835
454	4f¹¹5s²5p²	4f-5(5)5.4f+6(4)7.5p-1(1)6.5p+1(3)3	51.363160
455	4f¹²5s¹5p²	4f-5(5)5.4f+7(7)6.5s+1(1)5.5p-1(1)6.5p+1(3)5	51.370276
456	4f¹¹5s²5p²	4f-5(5)5.4f+6(4)7.5p-1(1)6.5p+1(3)7	51.373528
457	4f¹²5s¹5p²	4f+6(12)12.5s+1(1)13.5p-1(1)14.5p+1(3)17	51.564277
458	4f¹¹5s²5p²	4f-5(5)5.4f+6(4)7.5p-1(1)6.5p+1(3)5	51.616242
459	4f¹¹5s²5p²	4f-3(5)5.5p-1(1)6.5p+1(3)9	51.669738
460	4f¹³5s¹5p¹	4f-5(5)5.5s+1(1)6.5p+1(3)3	51.794518
461	4f¹²5s¹5p²	4f+6(12)12.5s+1(1)11.5p-1(1)12.5p+1(3)9	51.808742
462	4f¹¹5s²5p²	4f+5(15)15.5p+2(4)15	51.873567
463	4f¹¹5s²5p²	4f-4(4)4.4f+7(7)9.5p-1(1)10.5p+1(3)13	51.894895
464	4f¹¹5s²5p²	4f-3(5)5.5p-1(1)4.5p+1(3)7	51.949134
465	4f¹¹5s²5p²	4f-3(5)5.5p-1(1)4.5p+1(3)1	52.008321
466	4f¹²5s¹5p²	4f-5(5)5.4f+7(7)10.5s+1(1)9.5p-1(1)10.5p+1(3)7	52.026776
467	4f¹¹5s²5p²	4f-5(5)5.4f+6(4)7.5p-1(1)6.5p+1(3)5	52.033636
468	4f¹²5s¹5p²	4f-5(5)5.4f+7(7)8.5s+1(1)9.5p-1(1)8.5p+1(3)11	52.083735
469	4f¹²5s¹5p²	4f+6(4)4.5s+1(1)3.5p-1(1)4.5p+1(3)3	52.119437
470	4f¹¹5s²5p²	4f-3(5)5.5p-1(1)4.5p+1(3)3	52.127458
471	4f¹¹5s²5p²	4f-4(4)4.4f+7(7)9.5p-1(1)10.5p+1(3)11	52.249539
472	4f¹²5s¹5p²	4f-4(8)8.5s+1(1)7.5p-1(1)8.5p+1(3)5	52.272296
473	4f¹¹5s²5p²	4f+5(15)15.5p+2(4)13	52.359709
474	4f¹²5s¹5p²	4f+6(12)12.5s+1(1)13.5p-1(1)14.5p+1(3)15	52.368597
475	4f¹³5s¹5p¹	4f-5(5)5.5s+1(1)4.5p+1(3)7	52.414510
476	4f¹¹5s²5p²	4f+5(15)15.5p+2(4)11	52.547263
477	4f¹²5s¹5p²	4f+6(12)12.5s+1(1)11.5p-1(1)12.5p+1(3)13	52.589880
478	4f¹¹5s²5p²	4f-3(5)5.5p-1(1)4.5p+1(3)5	52.607852
479	4f¹²5s¹5p²	4f-5(5)5.4f+7(7)10.5s+1(1)9.5p-1(1)10.5p+1(3)9	52.686118
480	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)13.5p+2(4)17	52.735714
481	4f¹²5s¹5p²	4f+6(4)4.5s+1(1)3.5p-1(1)4.5p+1(3)1	52.825991
482	4f¹²5s¹5p²	4f+6(8)8.5s+1(1)7.5p-1(1)8.5p+1(3)5	52.888739
483	4f¹¹5s²5p²	4f-4(4)4.4f+7(7)9.5p-1(1)10.5p+1(3)9	52.889924
484	4f¹²5s¹5p²	4f+6(12)12.5s+1(1)13.5p-1(1)12.5p+1(3)11	52.905137
485	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)13.5p+2(4)15	53.036541
486	4f¹²5s¹5p²	4f+6(8)8.5s+1(1)9.5p-1(1)10.5p+1(3)13	53.151612
487	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)13.5p+2(4)13	53.161837
488	4f¹²5s¹5p²	4f-5(5)5.4f+7(7)8.5s+1(1)9.5p-1(1)8.5p+1(3)11	53.245023
489	4f¹²5s¹5p²	4f+6(8)8.5s+1(1)9.5p-1(1)10.5p+1(3)11	53.248825
490	4f¹²5s¹5p²	4f+6(12)12.5s+1(1)11.5p-1(1)10.5p+1(3)9	53.381515
491	4f¹²5s¹5p²	4f+6(8)8.5s+1(1)7.5p-1(1)8.5p+1(3)7	53.404688
492	4f¹¹5s²5p²	4f-4(4)4.4f+7(7)9.5p-1(1)8.5p+1(3)7	53.434223
493	4f¹³5s¹5p¹	4f-5(5)5.5s+1(1)6.5p+1(3)5	53.481890
494	4f¹²5s¹5p²	4f+6(12)12.5s+1(1)11.5p-1(1)10.5p+1(3)7	53.583051
495	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)13.5p+2(4)11	53.620775
496	4f¹¹5s²5p²	4f-5(5)5.4f+6(0)5.5p-1(1)6.5p+1(3)3	53.620908
497	4f¹¹5s²5p²	4f+5(9)9.5p+2(4)13	53.694318
498	4f¹¹5s²5p²	4f-5(5)5.4f+6(12)13.5p+2(4)9	53.695742
499	4f¹¹5s²5p²	4f+5(11)11.5p+2(4)15	53.722950
500	4f¹²5s¹5p²	4f+6(8)8.5s+1(1)7.5p-1(1)8.5p+1(3)9	53.767747
634	4f¹⁴5p¹	5p-1(1)1	58.282075
1292	4f¹⁴5p¹	5p+1(3)3	72.160271

Table 11. Comparison of energy levels (in Rydberg) calculated with FAC for Pm-like W with other available results.

Level No.	Configuration	2J	FAC	NIST	Safronova ^a
1	4f¹³5s²	5	0.1658	0.24(3) + x	0.165 ^b
43	4f¹⁴5s¹	1	1.8482	1.62(3) + y	1.79
91	4f¹³5s5p	9	2.2445	2.3379(12)	2.294
263	4f¹³5s5p	5	3.1756	3.350(3)	3.212
326	4f¹³5s5p	9	3.3200	3.490(3)	3.361
451	4f¹³5s5p	7	3.7536	3.826(3)	3.878

a—Reference [28]. b—Reference [32].

Table 12. Transition data for the 4f¹³5s^{2 2}F-4f¹³5s5p and 4f¹⁴5s-4f¹⁴5p transitions in Pm-like W. Oscillator strength are given in both the length form (gf_L) and velocity form (gf_v).

	4f¹³5s^{2 2}F-4f¹³5s5p Transition
j	2J_j	i	2J_i	λ(nm)	gf_L	gf_v	A_ji(s⁻¹) OUT3	A_ji(s⁻¹) OUTF	Type
69	7	0	7	44.1901	2.41E-02	2.20E-02	8.84E+07	1.03E+08	E1
69	7	1	5	48.0529	6.40E-04	8.21E-04	3.20E+06	2.31E+06	E1
69	7	0	7	44.1901	9.18E-12	9.18E-12	2.95E-02	3.92E-02	M2
69	7	1	5	48.0529	1.16E-12	1.16E-12	3.81E-03	4.18E-03	M2
85	7	0	7	41.2210	2.75E-01	2.40E-01	1.40E+09	1.35E+09	E1
85	7	1	5	44.5625	1.67E-02	1.68E-02	7.72E+07	7.02E+07	E1
85	7	0	7	41.2210	2.05E-12	2.05E-12	1.15E-02	1.01E-02	M2
85	7	1	5	44.5625	6.20E-14	6.20E-14	4.67E-04	2.60E-04	M2
89	5	0	7	40.9938	8.27E-02	7.26E-02	4.68E+08	5.47E+08	E1
89	5	1	5	44.2971	4.68E-03	4.16E-03	2.93E+07	2.65E+07	E1
89	5	0	7	40.9938	1.81E-12	1.81E-12	9.39E-03	1.19E-02	M2
89	5	1	5	44.2971	4.19E-12	4.19E-12	1.92E-02	2.38E-02	M2
91	9	0	7	40.6002	5.38E-01	5.00E-01	2.18E+09	2.18E+09	E1
91	9	0	7	40.6002	7.31E-12	7.31E-12	2.23E-02	2.96E-02	M2
91	9	1	5	43.8378	2.25E-12	2.25E-12	1.01E-02	7.81E-03	M2
94	5	0	7	39.7106	2.42E-01	2.19E-01	1.78E+09	1.71E+09	E1
94	5	1	5	42.8026	5.97E-02	5.49E-02	3.36E+08	3.62E+08	E1
94	5	0	7	39.7106	1.48E-11	1.48E-11	9.30E-02	1.04E-01	M2
94	5	1	5	42.8026	1.10E-13	1.10E-13	1.35E-03	6.68E-04	M2
108	5	0	7	37.4897	5.80E-02	5.69E-02	4.50E+08	4.59E+08	E1
108	5	1	5	40.2335	1.76E-01	1.50E-01	1.29E+09	1.21E+09	E1
108	5	0	7	37.4897	8.94E-13	8.94E-13	1.10E-02	7.07E-03	M2
108	5	1	5	40.2335	3.24E-12	3.24E-12	1.31E-02	2.22E-02	M2
110	7	0	7	37.3208	2.07E-02	1.76E-02	1.31E+08	1.24E+08	E1
110	7	1	5	40.0390	4.29E-01	3.86E-01	2.17E+09	2.23E+09	E1
110	7	0	7	37.3208	3.07E-12	3.07E-12	1.50E-02	1.84E-02	M2
110	7	1	5	40.0390	8.68E-12	8.68E-12	3.70E-02	4.51E-02	M2
114	3	1	5	39.6448	2.25E-01	1.95E-01	2.38E+09	2.38E+09	E1
114	3	0	7	36.9780	4.52E-12	4.52E-12	6.28E-02	5.51E-02	M2
114	3	1	5	39.6448	7.47E-12	7.47E-12	6.67E-02	7.93E-02	M2
222	11	0	7	29.5982	3.95E-09	3.95E-09	2.50E+01	2.51E+01	M2
250	3	1	5	30.5445	4.58E-03	3.26E-03	8.20E+07	8.18E+07	E1
250	3	0	7	28.9367	1.25E-09	1.25E-09	2.45E+01	2.48E+01	M2
250	3	1	5	30.5445	3.70E-10	3.70E-10	6.94E+00	6.62E+00	M2
263	5	0	7	28.6955	1.85E-02	1.53E-02	2.10E+08	2.50E+08	E1
263	5	1	5	30.2759	1.96E-02	1.80E-02	2.04E+08	2.37E+08	E1
263	5	0	7	28.6955	2.16E-09	2.16E-09	2.98E+01	2.92E+01	M2
263	5	1	5	30.2759	2.74E-10	2.74E-10	3.47E+00	3.32E+00	M2
266	1	1	5	30.2379	7.45E-10	7.45E-10	2.74E+01	2.72E+01	M2
277	7	0	7	28.4044	3.29E-02	3.06E-02	2.69E+08	3.40E+08	E1
277	7	1	5	29.9520	4.30E-03	4.51E-03	3.61E+07	4.00E+07	E1
277	7	0	7	28.4044	3.21E-09	3.21E-09	3.44E+01	3.32E+01	M2
277	7	1	5	29.9520	1.24E-10	1.24E-10	1.26E+00	1.15E+00	M2
279	9	0	7	28.3905	2.12E-02	1.76E-02	1.30E+08	1.75E+08	E1
279	9	0	7	28.3905	4.13E-09	4.13E-09	3.53E+01	3.42E+01	M2
279	9	1	5	29.9366	9.21E-11	9.21E-11	7.97E-01	6.85E-01	M2
317	3	1	5	28.9893	2.36E-02	2.32E-02	3.72E+08	4.68E+08	E1
317	3	0	7	27.5371	5.07E-10	5.07E-10	1.15E+01	1.12E+01	M2
317	3	1	5	28.9893	1.16E-09	1.16E-09	2.36E+01	2.30E+01	M2
326	9	0	7	27.4477	4.27E-02	4.56E-02	3.18E+08	3.78E+08	E1
326	9	0	7	27.4477	1.26E-10	1.26E-10	1.12E+00	1.12E+00	M2
326	9	1	5	28.8902	3.90E-09	3.90E-09	3.02E+01	3.12E+01	M2
351	5	0	7	26.9546	1.60E-02	1.60E-02	1.80E+08	2.45E+08	E1
351	5	1	5	28.3445	2.01E-03	2.06E-03	2.35E+07	2.79E+07	E1
351	5	0	7	26.9546	3.86E-10	3.86E-10	6.32E+00	5.91E+00	M2
351	5	1	5	28.3445	2.22E-09	2.22E-09	3.17E+01	3.07E+01	M2
357	7	0	7	26.8680	1.38E-02	1.33E-02	1.21E+08	1.59E+08	E1
357	7	1	5	28.2487	5.85E-02	5.66E-02	5.11E+08	6.11E+08	E1
357	7	0	7	26.8680	1.59E-10	1.59E-10	2.11E+00	1.84E+00	M2
357	7	1	5	28.2487	3.26E-09	3.26E-09	3.55E+01	3.41E+01	M2
433	5	0	7	24.8557	3.27E+00	3.03E+00	6.52E+10	5.88E+10	E1
433	5	1	5	26.0327	3.84E-02	3.41E-02	7.37E+08	6.29E+08	E1
433	5	0	7	24.8557	3.52E-14	3.52E-14	8.78E-04	6.33E-04	M2
433	5	1	5	26.0327	1.45E-11	1.45E-11	2.74E-01	2.38E-01	M2
434	9	0	7	24.8032	5.16E+00	4.84E+00	6.74E+10	5.59E+10	E1
434	9	0	7	24.8032	6.56E-12	6.56E-12	3.56E-03	7.11E-02	M2
434	9	1	5	25.9752	3.47E-11	3.47E-11	3.20E-01	3.43E-01	M2
451	7	0	7	24.2771	3.97E+00	3.75E+00	4.92E+10	5.62E+10	E1
451	7	1	5	25.3988	4.19E-01	4.00E-01	4.99E+09	5.42E+09	E1
451	7	0	7	24.2771	1.29E-11	1.29E-11	1.45E-01	1.83E-01	M2
451	7	1	5	25.3988	1.73E-12	1.73E-12	1.80E-02	2.23E-02	M2
460	3	1	5	25.0275	2.23E+00	2.06E+00	6.66E+10	5.93E+10	E1
460	3	0	7	23.9377	1.38E-12	1.38E-12	7.80E-02	4.03E-02	M2
460	3	1	5	25.0275	6.03E-12	6.03E-12	2.44E-01	1.61E-01	M2
475	7	0	7	23.6546	4.17E-01	3.92E-01	8.91E+09	6.21E+09	E1
475	7	1	5	24.7182	3.77E+00	3.54E+00	5.84E+10	5.14E+10	E1
475	7	0	7	23.6546	9.03E-12	9.03E-12	2.22E-01	1.35E-01	M2
475	7	1	5	24.7182	2.69E-11	2.69E-11	3.70E-01	3.66E-01	M2
493	5	0	7	23.1825	4.11E-02	3.86E-02	8.33E+08	8.51E+08	E1
493	5	1	5	24.2031	3.28E+00	3.09E+00	6.74E+10	6.23E+10	E1
493	5	0	7	23.1825	1.09E-11	1.09E-11	2.19E-01	2.26E-01	M2
493	5	1	5	24.2031	1.82E-12	1.82E-12	1.32E-02	3.45E-02	M2
	4f¹⁴5s-4f¹⁴5p transition
J	2J_j	i	2J_i	λ(in nm)	gf_L	gf_v	A_ji(s⁻¹) OUT3	A_ji(s⁻¹) OUTF	Type
634	1	43	1	37.4171	4.89E-01	4.61E-01	1.29E+10	1.16E+10	E1
1292	3	43	1	26.3718	1.33E+00	1.29E+00	3.50E+10	3.18E+10	E1
1292	3	43	1	26.3718	2.40E-09	2.40E-09	5.53E+01	5.75E+01	M2

Table 13. Comparison of a transition wavelength (in nm) calculated using FAC with NIST [9] and other results for Pm-like W. The indexes of the lower and upper levels, i and j, respectively, correspond to those given in Table 10.

i	J	λ (This Work)	λ (NIST)	λ (Others)
0	91	40.600	38.978(20)	---------
0	263	28.696	27.205(20)	---------
0	326	27.448	26.110(20)	---------
0	433	24.856	---------	24.91 ^c 24.70 ^a 24.71 ^b 24.76 ^d
0	434	24.803	---------	24.83 ^c 24.64 ^a 24.53 ^b 24.69 ^d
0	451	24.277	---------	24.32 ^c 24.06 ^a 23.95 ^b 24.17 ^d
1	451	25.399	25.384(20)

a—Reference [28] results using COWAN code. b—Reference [31] results using the HULLAC code. c—Experimental results of Reference [31]. d—Reference [33] using FAC.

Table 14. Comparison of transition wavelength (nm) calculated with FAC for the transition 4f¹³5s^{2 2}F_5/2-²F_7/2 with other results for Pm-like W. Experimental wavelengths are given in standard air, while theoretically calculated wavelengths are in vacuum.

Method	Wavelength (nm)
FAC (this work)	549.72
Experiment ^f	560.25
Experiment ^a	549.95 ± 0.06
RMBPT ^a	567.64
FAC ^a	552.08
Safronova et al. (COWAN) ^b	537.63
Vilkas et al. (MR-MP) ^c	388.71
Nandy (CCSD-T) ^d	556.60
FAC ^e	550.80

a—Reference [32]. b—Reference [28]. c—Reference [24]. d—Reference [38]. e—Reference [33]. f—Reference [31].

Table 15. Collisional excitation cross-sections (100 Mb) of Pm-like W from the ground state to various levels.

Energy (eV) /Transition	0–2	0–3	0–4	Energy (eV) /Transition	0–5	0–6	0–7	Energy (eV) /Transition	0–43
0.00E+00	2.54E+04	2.54E+04	2.54E+04	0.00E+00	2.54E+04	2.54E+04	2.54E+04	0.00E+00	3.00E+04
3.72E-01	1.72E+02	1.12E+02	8.80E+01	3.72E-01	8.14E+01	5.64E+01	1.13E+02	1.20E+00	3.06E+01
1.32E+01	5.98E+01	4.14E+01	3.36E+01	1.32E+01	3.19E+01	2.35E+01	4.93E+01	2.43E+01	1.52E+01
4.70E+01	1.89E+01	1.37E+01	1.11E+01	4.70E+01	1.07E+01	8.24E+00	1.91E+01	6.85E+01	7.18E+00
1.36E+02	4.65E+00	3.87E+00	2.93E+00	1.36E+02	2.94E+00	2.36E+00	6.91E+00	1.52E+02	3.21E+00
3.64E+02	8.57E-01	1.10E+00	6.36E-01	3.64E+02	7.57E-01	6.19E-01	2.54E+00	3.11E+02	1.47E+00
9.32E+02	1.97E-01	4.12E-01	1.85E-01	9.32E+02	2.63E-01	1.96E-01	9.75E-01	6.04E+02	7.42E-01
Energy (eV) /Transition	0–8	0–9	0–10	0–11	Energy (eV) /Transition	0–12	0–13	0–14	0–15
0.00E+00	2.54E+04	2.54E+04	2.54E+04	2.54E+04	0.00E+00	2.54E+04	2.54E+04	2.54E+04	2.54E+04
7.44E-01	4.67E+01	2.78E+01	2.96E+01	1.50E+02	7.44E-01	7.69E+01	1.78E+02	1.77E+01	1.62E+01
2.11E+01	1.64E+01	9.12E+00	9.88E+00	5.42E+01	2.11E+01	2.77E+01	6.76E+01	6.84E+00	6.19E+00
6.78E+01	6.91E+00	3.02E+00	3.32E+00	2.17E+01	6.78E+01	1.08E+01	2.78E+01	2.76E+00	2.22E+00
1.74E+02	3.25E+00	9.09E-01	1.01E+00	9.12E+00	1.74E+02	4.27E+00	1.20E+01	1.14E+00	7.23E-01
4.13E+02	1.71E+00	2.85E-01	3.13E-01	3.99E+00	4.13E+02	1.79E+00	5.32E+00	4.88E-01	2.44E-01
9.32E+02	7.91E-01	1.11E-01	1.21E-01	1.78E+00	9.32E+02	7.87E-01	2.39E+00	2.16E-01	9.65E-02
Energy (eV) /Transition	0–16	0–17	0–18	0–19	0–20	0–21	0–22	0–23	0–24
0.00E+00	2.54E+04	2.54E+04	2.54E+04	2.54E+04	2.54E+04	2.54E+04	2.54E+04	2.54E+04	2.54E+04
7.44E-01	1.11E+01	4.92E+01	3.25E+01	5.56E+00	6.88E+00	2.18E+02	3.76E+01	3.07E+01	2.40E+01
2.11E+01	4.71E+00	2.02E+01	1.24E+01	2.16E+00	2.69E+00	9.61E+01	1.69E+01	1.39E+01	1.11E+01
6.78E+01	2.09E+00	8.33E+00	4.08E+00	7.25E-01	9.17E-01	4.22E+01	7.40E+00	6.13E+00	4.98E+00
1.74E+02	9.88E-01	3.47E+00	1.03E+00	1.94E-01	2.52E-01	1.87E+01	3.23E+00	2.68E+00	2.23E+00
4.13E+02	4.94E-01	1.50E+00	2.12E-01	4.75E-02	6.39E-02	8.42E+00	1.44E+00	1.20E+00	1.01E+00
9.32E+02	2.44E-01	6.68E-01	5.14E-02	1.49E-02	2.12E-02	3.81E+00	6.48E-01	5.38E-01	4.57E-01
Energy (eV) /Transition	0–26	0–27	0–28	0–30	0–31	0–32	0–33	0–36	0–37
0.00E+00	2.54E+04	2.54E+04	2.54E+04	2.54E+04	2.54E+04	2.54E+04	2.54E+04	2.54E+04	2.54E+04
1.48E+00	3.44E+01	6.29E+01	1.73E+02	1.83E+00	2.50E+01	1.63E+01	5.08E+01	4.80E+01	2.57E+01
3.30E+01	1.15E+01	2.58E+01	7.67E+01	7.06E-01	9.14E+00	5.97E+00	2.20E+01	2.14E+01	1.03E+01
9.59E+01	3.46E+00	1.12E+01	3.69E+01	2.67E-01	3.15E+00	2.03E+00	1.00E+01	1.01E+01	4.20E+00
2.21E+02	8.42E-01	5.07E+00	1.86E+01	9.95E-02	1.05E+00	6.36E-01	4.81E+00	4.99E+00	1.79E+00
4.66E+02	1.97E-01	2.47E+00	9.59E+00	4.19E-02	4.11E-01	2.25E-01	2.41E+00	2.54E+00	8.53E-01
9.32E+02	4.72E-02	1.24E+00	4.96E+00	2.09E-02	1.96E-01	9.44E-02	1.23E+00	1.31E+00	4.40E-01
Energy (eV) /Transition	0–38	0–39	0–41	0–42	0–45	0–46	0–47	0–49	0–50
0.00E+00	2.54E+04	2.54E+04	2.54E+04	2.54E+04	2.54E+04	2.54E+04	2.54E+04	2.54E+04	2.54E+04
1.48E+00	1.38E+01	5.47E+01	7.00E+01	1.12E+01	3.03E+01	2.14E+01	1.31E+01	2.71E+01	3.43E+01
3.30E+01	5.39E+00	2.42E+01	3.25E+01	4.53E+00	1.38E+01	9.78E+00	5.37E+00	1.25E+01	1.63E+01
9.59E+01	2.10E+00	1.12E+01	1.60E+01	1.77E+00	6.51E+00	4.63E+00	2.18E+00	6.04E+00	8.19E+00
2.21E+02	8.62E-01	5.46E+00	8.18E+00	6.91E-01	3.20E+00	2.28E+00	9.22E-01	3.02E+00	4.41E+00
4.66E+02	4.12E-01	2.75E+00	4.26E+00	3.02E-01	1.63E+00	1.16E+00	4.41E-01	1.55E+00	2.57E+00
9.32E+02	2.19E-01	1.41E+00	2.22E+00	1.46E-01	8.42E-01	5.99E-01	2.30E-01	7.99E-01	1.54E+00
Energy (eV) /Transition	0–25	0–29	0–34	0–35	0–40	0–44	0–48	Energy (eV) /Transition	0–1
0.00E+00	2.54E+04	2.54E+04	2.54E+04	2.54E+04	2.54E+04	2.54E+04	2.54E+04	0.00E+00	3.00E+04
1.40E+00	1.37E-01	1.56E-01	9.11E+00	7.74E-01	1.50E-01	2.15E-01	1.30E+00	1.13E-01	2.79E+03
4.18E+01	3.78E-02	5.01E-02	2.89E+00	2.69E-01	6.03E-02	8.22E-02	5.14E-01	2.21E+00	1.47E+03
1.37E+02	8.92E-03	1.55E-02	8.48E-01	9.60E-02	2.57E-02	3.25E-02	2.12E-01	6.17E+00	7.72E+02
3.58E+02	1.66E-03	4.96E-03	2.65E-01	3.77E-02	1.13E-02	1.35E-02	9.14E-02	1.36E+01	4.02E+02
8.57E+02	2.51E-04	1.89E-03	1.01E-01	1.63E-02	5.00E-03	5.83E-03	4.03E-02	2.77E+01	2.06E+02
1.91E+03	3.28E-05	8.74E-04	4.29E-02	7.56E-03	2.28E-03	2.66E-03	1.84E-02	5.41E+01	1.03E+02

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Singh, N.; Aggarwal, S.; Mohan, M. Extended Atomic Structure Calculations for W¹¹⁺ and W¹³⁺. Atoms 2020, 8, 92. https://0-doi-org.brum.beds.ac.uk/10.3390/atoms8040092

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Singh N, Aggarwal S, Mohan M. Extended Atomic Structure Calculations for W¹¹⁺ and W¹³⁺. Atoms. 2020; 8(4):92. https://0-doi-org.brum.beds.ac.uk/10.3390/atoms8040092

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Singh, Narendra, Sunny Aggarwal, and Man Mohan. 2020. "Extended Atomic Structure Calculations for W¹¹⁺ and W¹³⁺" Atoms 8, no. 4: 92. https://0-doi-org.brum.beds.ac.uk/10.3390/atoms8040092

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Extended Atomic Structure Calculations for W¹¹⁺ and W¹³⁺

Abstract

1. Introduction